Quantum key distribution ( QKD ) is a secure communication method that implements a cryptographic protocol involving components of quantum mechanics . It enables two parties to produce a shared random secret key known only to them, which then can be used to encrypt and decrypt messages . The process of quantum key distribution is not to be confused with quantum cryptography , as it is the best-known example of a quantum-cryptographic task.
173-547: An important and unique property of quantum key distribution is the ability of the two communicating users to detect the presence of any third party trying to gain knowledge of the key. This results from a fundamental aspect of quantum mechanics: the process of measuring a quantum system in general disturbs the system. A third party trying to eavesdrop on the key must in some way measure it, thus introducing detectable anomalies. By using quantum superpositions or quantum entanglement and transmitting information in quantum states ,
346-433: A source of information. A memoryless source is one in which each message is an independent identically distributed random variable , whereas the properties of ergodicity and stationarity impose less restrictive constraints. All such sources are stochastic . These terms are well studied in their own right outside information theory. Information rate is the average entropy per symbol. For memoryless sources, this
519-507: A NAVIC receiver for time synchronization between the transmitter and receiver modules. Later in January 2022, Indian scientists were able to successfully create an atmospheric channel for exchange of crypted messages and images. After demonstrating quantum communication between two ground stations, India has plans to develop Satellite Based Quantum Communication (SBQC). In July 2022, researchers published their work experimentally implementing
692-418: A perfect vacuum, which they sometimes simply call "vacuum" or free space , and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space . In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term in vacuo is used to describe an object that
865-457: A relative permittivity and relative permeability that are not identically unity. In the theory of classical electromagnetism, free space has the following properties: The vacuum of classical electromagnetism can be viewed as an idealized electromagnetic medium with the constitutive relations in SI units: relating the electric displacement field D to the electric field E and
1038-552: A symmetric key of sufficient length or public keys of sufficient security level. With such information already available, in practice one can achieve authenticated and sufficiently secure communication without using QKD, such as by using the Galois/Counter Mode of the Advanced Encryption Standard . Thus QKD does the work of a stream cipher at many times the cost. Quantum key distribution
1211-608: A 148.7 km of optic fibre using the BB84 protocol. Significantly, this distance is long enough for almost all the spans found in today's fibre networks. A European collaboration achieved free space QKD over 144 km between two of the Canary Islands using entangled photons (the Ekert scheme) in 2006, and using BB84 enhanced with decoy states in 2007. As of August 2015 the longest distance for optical fiber (307 km)
1384-432: A Bell test to check that a device is working properly. Bell's theorem ensures that a device can create two outcomes that are exclusively correlated, meaning that Eve could not intercept the results, without making any assumptions about said device. This requires highly entangled states, and a low quantum bit error rate. DIQKD presents difficulties in creating qubits that are in such high quality entangled states, which makes it
1557-486: A Bell-basis measurement is performed and the ions are projected to a highly entangled state. Finally the qubits are returned to new locations in the ion traps disconnected from the optical link so that no information can be leaked. This is repeated many times before the key distribution proceeds. A separate experiment published in July 2022 demonstrated implementation of DIQKD that also uses a Bell inequality test to ensure that
1730-508: A box of matches. National Quantum-Safe Network Plus (NQSN+) was launched by IMDA in 2023 and is part of Singapore's Digital Connectivity Blueprint, which outlines the next bound of Singapore's digital connectivity to 2030. NQSN+ will support network operators to deploy quantum-safe networks nationwide, granting businesses easy access to quantum-safe solutions that safeguard their critical data. The NQSN+ will start with two network operators, Singtel and SPTel, together with SpeQtral. Each will build
1903-473: A challenge to realize experimentally. Twin fields quantum key distribution (TFQKD) was introduced in 2018, and is a version of DIQKD designed to overcome the fundamental rate-distance limit of traditional quantum key distribution. The rate-distance limit, also known as the rate-loss trade off, describes how as distance increases between Alice and Bob, the rate of key generation decreases exponentially. In traditional QKD protocols, this decay has been eliminated via
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#17327977312422076-486: A communication system can be implemented that detects eavesdropping. If the level of eavesdropping is below a certain threshold, a key can be produced that is guaranteed to be secure (i.e., the eavesdropper has no information about it). Otherwise no secure key is possible, and communication is aborted. The security of encryption that uses quantum key distribution relies on the foundations of quantum mechanics, in contrast to traditional public key cryptography , which relies on
2249-534: A continuous-variable QKD system through commercial fiber networks in Xi'an and Guangzhou over distances of 30.02 km (12.48 dB) and 49.85 km (11.62 dB) respectively. In December 2020, Indian Defence Research and Development Organisation tested a QKD between two of its laboratories in Hyderabad facility. The setup also demonstrated the validation of detection of a third party trying to gain knowledge of
2422-569: A device-independent quantum key distribution (DIQKD) protocol that uses quantum entanglement (as suggested by Ekert) to insure resistance to quantum hacking attacks. They were able to create two ions, about two meters apart that were in a high quality entangled state using the following process: Alice and Bob each have ion trap nodes with an Sr qubit inside. Initially, they excite the ions to an electronic state, which creates an entangled state. This process also creates two photons, which are then captured and transported using an optical fiber, at which point
2595-579: A fundamental limit within which instantaneous position and momentum , or energy and time can be measured. This far reaching consequences also threatened whether the "emptiness" of space between particles exists. The strictest criterion to define a vacuum is a region of space and time where all the components of the stress–energy tensor are zero. This means that this region is devoid of energy and momentum, and by consequence, it must be empty of particles and other physical fields (such as electromagnetism) that contain energy and momentum. In general relativity ,
2768-604: A good model for realizable vacuum, and agrees with a number of experimental observations as described next. QED vacuum has interesting and complex properties. In QED vacuum, the electric and magnetic fields have zero average values, but their variances are not zero. As a result, QED vacuum contains vacuum fluctuations ( virtual particles that hop into and out of existence), and a finite energy called vacuum energy . Vacuum fluctuations are an essential and ubiquitous part of quantum field theory. Some experimentally verified effects of vacuum fluctuations include spontaneous emission and
2941-422: A group at Shanghai Jiaotong University experimentally demonstrate that polarization quantum states including general qubits of single photon and entangled states can survive well after travelling through seawater, representing the first step towards underwater quantum communication. In May 2019 a group led by Hong Guo at Peking University and Beijing University of Posts and Telecommunications reported field tests of
3114-432: A mass spectrometer must be used in conjunction with the ionization gauge for accurate measurement. Vacuum is useful in a variety of processes and devices. Its first widespread use was in the incandescent light bulb to protect the filament from chemical degradation. The chemical inertness produced by a vacuum is also useful for electron beam welding , cold welding , vacuum packing and vacuum frying . Ultra-high vacuum
3287-479: A measurable vacuum relative to the local environment. Similarly, much higher than normal relative vacuum readings are possible deep in the Earth's ocean. A submarine maintaining an internal pressure of 1 atmosphere submerged to a depth of 10 atmospheres (98 metres; a 9.8-metre column of seawater has the equivalent weight of 1 atm) is effectively a vacuum chamber keeping out the crushing exterior water pressures, though
3460-448: A measurement in bytes per symbol, and a logarithm of base 10 will produce a measurement in decimal digits (or hartleys ) per symbol. Intuitively, the entropy H X of a discrete random variable X is a measure of the amount of uncertainty associated with the value of X when only its distribution is known. The entropy of a source that emits a sequence of N symbols that are independent and identically distributed (iid)
3633-447: A minute drag on the Earth's orbit. While the Earth does, in fact, move through a relatively dense medium in comparison to that of interstellar space, the drag is so minuscule that it could not be detected. In 1912, astronomer Henry Pickering commented: "While the interstellar absorbing medium may be simply the ether, [it] is characteristic of a gas, and free gaseous molecules are certainly there". Thereafter, however, luminiferous aether
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#17327977312423806-473: A nationwide, interoperable quantum-safe network that can serve all businesses. Businesses can work with NQSN+ operators to integrate quantum-safe solutions such as Quantum Key Distribution (QKD) and Post-Quantum Cryptography (PQC) and be secure in the quantum age. In 2024, the ESA plans to launch the satellite Eagle-1, an experimental space-based quantum key distribution system. The simplest type of possible attack
3979-416: A new, shorter key, in such a way that Eve has only negligible information about the new key. This is performed using a randomness extractor , for example, by applying a universal hash function , chosen at random from a publicly known set of such functions, which takes as its input a binary string of length equal to the key and outputs a binary string of a chosen shorter length. The amount by which this new key
4152-405: A partial vacuum of about 10 Pa (0.1 Torr ). A number of electrical properties become observable at this vacuum level, which renewed interest in further research. While outer space provides the most rarefied example of a naturally occurring partial vacuum, the heavens were originally thought to be seamlessly filled by a rigid indestructible material called aether . Borrowing somewhat from
4325-426: A proposed propulsion system for interplanetary travel . All of the observable universe is filled with large numbers of photons , the so-called cosmic background radiation , and quite likely a correspondingly large number of neutrinos . The current temperature of this radiation is about 3 K (−270.15 °C ; −454.27 °F ). The quality of a vacuum is indicated by the amount of matter remaining in
4498-467: A public classical channel, for example using broadcast radio or the internet. The protocol is designed with the assumption that an eavesdropper (referred to as Eve) can interfere in any way with the quantum channel, while the classical channel needs to be authenticated . The security of the protocol comes from encoding the information in non-orthogonal states . Quantum indeterminacy means that these states cannot in general be measured without disturbing
4671-442: A random variable with two outcomes is the binary entropy function, usually taken to the logarithmic base 2, thus having the shannon (Sh) as unit: The joint entropy of two discrete random variables X and Y is merely the entropy of their pairing: ( X , Y ) . This implies that if X and Y are independent , then their joint entropy is the sum of their individual entropies. For example, if ( X , Y ) represents
4844-476: A randomly phase p a or p b in the interval [0, 2π) and an encoding phase γ a or γ b . The pulses are sent along a quantum to Charlie, a third party who can be malicious or not. Charlie uses a beam splitter to overlap the two pulses and perform a measurement. He has two detectors in his own lab, one of which will light up if the bits are equal (00) or (11), and the other when they are different (10, 01). Charlie will announce to Alice and Bob which of
5017-526: A signal; noise, periods of silence, and other forms of signal corruption often degrade quality. Free space A vacuum ( pl. : vacuums or vacua ) is space devoid of matter . The word is derived from the Latin adjective vacuus (neuter vacuum ) meaning "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure . Physicists often discuss ideal test results that would occur in
5190-400: A single random variable. Another useful concept is mutual information defined on two random variables, which describes the measure of information in common between those variables, which can be used to describe their correlation. The former quantity is a property of the probability distribution of a random variable and gives a limit on the rate at which data generated by independent samples with
5363-447: A statistical description for data, information theory quantifies the number of bits needed to describe the data, which is the information entropy of the source. This division of coding theory into compression and transmission is justified by the information transmission theorems, or source–channel separation theorems that justify the use of bits as the universal currency for information in many contexts. However, these theorems only hold in
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5536-486: A theoretical section quantifying "intelligence" and the "line speed" at which it can be transmitted by a communication system, giving the relation W = K log m (recalling the Boltzmann constant ), where W is the speed of transmission of intelligence, m is the number of different voltage levels to choose from at each time step, and K is a constant. Ralph Hartley 's 1928 paper, Transmission of Information , uses
5709-511: A unit or scale or measure of information. Alan Turing in 1940 used similar ideas as part of the statistical analysis of the breaking of the German second world war Enigma ciphers. Much of the mathematics behind information theory with events of different probabilities were developed for the field of thermodynamics by Ludwig Boltzmann and J. Willard Gibbs . Connections between information-theoretic entropy and thermodynamic entropy, including
5882-432: A useful scale. TFQKD aims to bypass the rate-distance limit without the use of quantum repeaters or relay nodes, creating manageable levels of noise and a process that can be repeated much more easily with today's existing technology. The original protocol for TFQKD is as follows: Alice and Bob each have a light source and one arm on an interferometer in their laboratories. The light sources create two dim optical pulses with
6055-477: A vacuum if he wanted and the 1277 Paris condemnations of Bishop Étienne Tempier , which required there to be no restrictions on the powers of God, led to the conclusion that God could create a vacuum if he so wished. From the 14th century onward increasingly departed from the Aristotelian perspective, scholars widely acknowledged that a supernatural void exists beyond the confines of the cosmos itself by
6228-430: A vacuum is called outgassing . All materials, solid or liquid, have a small vapour pressure , and their outgassing becomes important when the vacuum pressure falls below this vapour pressure. Outgassing has the same effect as a leak and will limit the achievable vacuum. Outgassing products may condense on nearby colder surfaces, which can be troublesome if they obscure optical instruments or react with other materials. This
6401-400: A vacuum was present, if only for an instant, between two flat plates when they were rapidly separated. There was much discussion of whether the air moved in quickly enough as the plates were separated, or, as Walter Burley postulated, whether a 'celestial agent' prevented the vacuum arising. Jean Buridan reported in the 14th century that teams of ten horses could not pull open bellows when
6574-549: A vanishing stress–energy tensor implies, through Einstein field equations , the vanishing of all the components of the Ricci tensor . Vacuum does not mean that the curvature of space-time is necessarily flat: the gravitational field can still produce curvature in a vacuum in the form of tidal forces and gravitational waves (technically, these phenomena are the components of the Weyl tensor ). The black hole (with zero electric charge)
6747-467: A violation of Bell inequality by 2.37 ± 0.09 under strict Einstein locality conditions" along a "summed length varying from 1600 to 2400 kilometers." Later that year BB84 was successfully implemented over satellite links from Micius to ground stations in China and Austria. The keys were combined and the result was used to transmit images and video between Beijing, China, and Vienna, Austria. In August 2017,
6920-515: A wide array of vacuum technologies has since become available. The development of human spaceflight has raised interest in the impact of vacuum on human health, and on life forms in general. The word vacuum comes from Latin 'an empty space, void', noun use of neuter of vacuus , meaning "empty", related to vacare , meaning "to be empty". Vacuum is one of the few words in the English language that contains two consecutive instances of
7093-433: Is N ⋅ H bits (per message of N symbols). If the source data symbols are identically distributed but not independent, the entropy of a message of length N will be less than N ⋅ H . If one transmits 1000 bits (0s and 1s), and the value of each of these bits is known to the receiver (has a specific value with certainty) ahead of transmission, it is clear that no information is transmitted. If, however, each bit
Quantum key distribution - Misplaced Pages Continue
7266-408: Is symmetric : Mutual information can be expressed as the average Kullback–Leibler divergence (information gain) between the posterior probability distribution of X given the value of Y and the prior distribution on X : In other words, this is a measure of how much, on the average, the probability distribution on X will change if we are given the value of Y . This is often recalculated as
7439-441: Is a form of error correction carried out between Alice and Bob's keys, in order to ensure both keys are identical. It is conducted over the public channel and as such it is vital to minimise the information sent about each key, as this can be read by Eve. A common protocol used for information reconciliation is the cascade protocol , proposed in 1994. This operates in several rounds, with both keys divided into blocks in each round and
7612-516: Is a non-SI unit): Vacuum is measured in units of pressure , typically as a subtraction relative to ambient atmospheric pressure on Earth. But the amount of relative measurable vacuum varies with local conditions. On the surface of Venus , where ground-level atmospheric pressure is much higher than on Earth, much higher relative vacuum readings would be possible. On the surface of the Moon with almost no atmosphere, it would be extremely difficult to create
7785-404: Is a way of comparing two distributions: a "true" probability distribution p ( X ) {\displaystyle p(X)} , and an arbitrary probability distribution q ( X ) {\displaystyle q(X)} . If we compress data in a manner that assumes q ( X ) {\displaystyle q(X)}
7958-515: Is an elegant example of a region completely "filled" with vacuum, but still showing a strong curvature. In classical electromagnetism , the vacuum of free space , or sometimes just free space or perfect vacuum , is a standard reference medium for electromagnetic effects. Some authors refer to this reference medium as classical vacuum , a terminology intended to separate this concept from QED vacuum or QCD vacuum , where vacuum fluctuations can produce transient virtual particle densities and
8131-427: Is an even higher-quality vacuum, with the equivalent of just a few hydrogen atoms per cubic meter on average in intergalactic space. Vacuum has been a frequent topic of philosophical debate since ancient Greek times, but was not studied empirically until the 17th century. Clemens Timpler (1605) philosophized about the experimental possibility of producing a vacuum in small tubes. Evangelista Torricelli produced
8304-538: Is connected to the region of interest. Any fluid can be used, but mercury is preferred for its high density and low vapour pressure. Simple hydrostatic gauges can measure pressures ranging from 1 torr (100 Pa) to above atmospheric. An important variation is the McLeod gauge which isolates a known volume of vacuum and compresses it to multiply the height variation of the liquid column. The McLeod gauge can measure vacuums as high as 10 torr (0.1 mPa), which
8477-466: Is defined as: It is common in information theory to speak of the "rate" or "entropy" of a language. This is appropriate, for example, when the source of information is English prose. The rate of a source of information is related to its redundancy and how well it can be compressed, the subject of source coding . Communications over a channel is the primary motivation of information theory. However, channels often fail to produce exact reconstruction of
8650-434: Is equal to the displacement of a millimeter of mercury ( mmHg ) in a manometer with 1 torr equaling 133.3223684 pascals above absolute zero pressure. Vacuum is often also measured on the barometric scale or as a percentage of atmospheric pressure in bars or atmospheres . Low vacuum is often measured in millimeters of mercury (mmHg) or pascals (Pa) below standard atmospheric pressure. "Below atmospheric" means that
8823-467: Is important in communication where it can be used to maximize the amount of information shared between sent and received signals. The mutual information of X relative to Y is given by: where SI ( S pecific mutual Information) is the pointwise mutual information . A basic property of the mutual information is that That is, knowing Y , we can save an average of I ( X ; Y ) bits in encoding X compared to not knowing Y . Mutual information
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#17327977312428996-466: Is independently equally likely to be 0 or 1, 1000 shannons of information (more often called bits) have been transmitted. Between these two extremes, information can be quantified as follows. If X {\displaystyle \mathbb {X} } is the set of all messages { x 1 , ..., x n } that X could be, and p ( x ) is the probability of some x ∈ X {\displaystyle x\in \mathbb {X} } , then
9169-435: Is merely the entropy of each symbol, while, in the case of a stationary stochastic process, it is: that is, the conditional entropy of a symbol given all the previous symbols generated. For the more general case of a process that is not necessarily stationary, the average rate is: that is, the limit of the joint entropy per symbol. For stationary sources, these two expressions give the same result. The information rate
9342-454: Is not symmetric and does not satisfy the triangle inequality (making it a semi-quasimetric). Another interpretation of the KL divergence is the "unnecessary surprise" introduced by a prior from the truth: suppose a number X is about to be drawn randomly from a discrete set with probability distribution p ( x ) {\displaystyle p(x)} . If Alice knows
9515-766: Is not symmetric. The I ( X n → Y n ) {\displaystyle I(X^{n}\to Y^{n})} measures the information bits that are transmitted causally from X n {\displaystyle X^{n}} to Y n {\displaystyle Y^{n}} . The Directed information has many applications in problems where causality plays an important role such as capacity of channel with feedback, capacity of discrete memoryless networks with feedback, gambling with causal side information, compression with causal side information, real-time control communication settings, and in statistical physics. Other important information theoretic quantities include
9688-573: Is not used. High vacuum systems must be clean and free of organic matter to minimize outgassing. Ultra-high vacuum systems are usually baked, preferably under vacuum, to temporarily raise the vapour pressure of all outgassing materials and boil them off. Once the bulk of the outgassing materials are boiled off and evacuated, the system may be cooled to lower vapour pressures and minimize residual outgassing during actual operation. Some systems are cooled well below room temperature by liquid nitrogen to shut down residual outgassing and simultaneously cryopump
9861-419: Is of great concern to space missions, where an obscured telescope or solar cell can ruin an expensive mission. The most prevalent outgassing product in vacuum systems is water absorbed by chamber materials. It can be reduced by desiccating or baking the chamber, and removing absorbent materials. Outgassed water can condense in the oil of rotary vane pumps and reduce their net speed drastically if gas ballasting
10034-770: Is often also used with encryption using symmetric key algorithms like the Advanced Encryption Standard algorithm. Quantum communication involves encoding information in quantum states, or qubits , as opposed to classical communication's use of bits . Usually, photons are used for these quantum states. Quantum key distribution exploits certain properties of these quantum states to ensure its security. There are several different approaches to quantum key distribution, but they can be divided into two main categories depending on which property they exploit. These two approaches can each be further divided into three families of protocols: discrete variable, continuous variable and distributed phase reference coding. Discrete variable protocols were
10207-437: Is referred to as ' QED vacuum ' to distinguish it from the vacuum of quantum chromodynamics , denoted as QCD vacuum . QED vacuum is a state with no matter particles (hence the name), and no photons . As described above, this state is impossible to achieve experimentally. (Even if every matter particle could somehow be removed from a volume, it would be impossible to eliminate all the blackbody photons .) Nonetheless, it provides
10380-626: Is represented by researchers from the Austrian Institute of Technology (AIT), the Institute for Quantum Optics and Quantum Information (IQOQI) and the University of Vienna . A hub-and-spoke network has been operated by Los Alamos National Laboratory since 2011. All messages are routed via the hub. The system equips each node in the network with quantum transmitters—i.e., lasers—but not with expensive and bulky photon detectors. Only
10553-581: Is shortened is calculated, based on how much information Eve could have gained about the old key (which is known due to the errors this would introduce), in order to reduce the probability of Eve having any knowledge of the new key to a very low value. In 1991, John Rarity , Paul Tapster and Artur Ekert , researchers from the UK Defence Research Agency in Malvern and Oxford University, demonstrated quantum key distribution protected by
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#173279773124210726-538: Is surrounded by a vacuum. The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. But higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, physics, and engineering, operate below one trillionth (10 ) of atmospheric pressure (100 nPa), and can reach around 100 particles/cm . Outer space
10899-428: Is the { | ↑ ⟩ , | → ⟩ } {\displaystyle \{|{\uparrow }\rangle ,\;|{\rightarrow }\rangle \}} basis rotated by θ {\displaystyle \theta } . They keep their series of basis choices private until measurements are completed. Two groups of photons are made: the first consists of photons measured using
11072-429: Is the conditional mutual information I ( X 1 , X 2 , . . . , X i ; Y i | Y 1 , Y 2 , . . . , Y i − 1 ) {\displaystyle I(X_{1},X_{2},...,X_{i};Y_{i}|Y_{1},Y_{2},...,Y_{i-1})} . In contrast to mutual information, directed information
11245-474: Is the average conditional entropy over Y : Because entropy can be conditioned on a random variable or on that random variable being a certain value, care should be taken not to confuse these two definitions of conditional entropy, the former of which is in more common use. A basic property of this form of conditional entropy is that: Mutual information measures the amount of information that can be obtained about one random variable by observing another. It
11418-458: Is the distribution underlying some data, when, in reality, p ( X ) {\displaystyle p(X)} is the correct distribution, the Kullback–Leibler divergence is the number of average additional bits per datum necessary for compression. It is thus defined Although it is sometimes used as a 'distance metric', KL divergence is not a true metric since it
11591-429: Is the intercept-resend attack, where Eve measures the quantum states (photons) sent by Alice and then sends replacement states to Bob, prepared in the state she measures. In the BB84 protocol, this produces errors in the key Alice and Bob share. As Eve has no knowledge of the basis a state sent by Alice is encoded in, she can only guess which basis to measure in, in the same way as Bob. If she chooses correctly, she measures
11764-454: Is the lowest direct measurement of pressure that is possible with current technology. Other vacuum gauges can measure lower pressures, but only indirectly by measurement of other pressure-controlled properties. These indirect measurements must be calibrated via a direct measurement, most commonly a McLeod gauge. The kenotometer is a particular type of hydrostatic gauge, typically used in power plants using steam turbines. The kenotometer measures
11937-443: Is used in the study of atomically clean substrates, as only a very good vacuum preserves atomic-scale clean surfaces for a reasonably long time (on the order of minutes to days). High to ultra-high vacuum removes the obstruction of air, allowing particle beams to deposit or remove materials without contamination. This is the principle behind chemical vapor deposition , physical vapor deposition , and dry etching which are essential to
12110-415: Is used to produce and distribute only a key, not to transmit any message data. This key can then be used with any chosen encryption algorithm to encrypt (and decrypt) a message, which can then be transmitted over a standard communication channel . The algorithm most commonly associated with QKD is the one-time pad , as it is provably secure when used with a secret, random key. In real-world situations, it
12283-581: Is used. A common unit of information is the bit or shannon , based on the binary logarithm . Other units include the nat , which is based on the natural logarithm , and the decimal digit , which is based on the common logarithm . In what follows, an expression of the form p log p is considered by convention to be equal to zero whenever p = 0 . This is justified because lim p → 0 + p log p = 0 {\displaystyle \lim _{p\rightarrow 0+}p\log p=0} for any logarithmic base. Based on
12456-412: Is useful for flywheel energy storage and ultracentrifuges . Vacuums are commonly used to produce suction , which has an even wider variety of applications. The Newcomen steam engine used vacuum instead of pressure to drive a piston. In the 19th century, vacuum was used for traction on Isambard Kingdom Brunel 's experimental atmospheric railway . Vacuum brakes were once widely used on trains in
12629-475: The Heading Indicator (HI) ) are typically vacuum-powered, as protection against loss of all (electrically powered) instruments, since early aircraft often did not have electrical systems, and since there are two readily available sources of vacuum on a moving aircraft, the engine and an external venturi. Vacuum induction melting uses electromagnetic induction within a vacuum. Maintaining a vacuum in
12802-623: The Institute for Quantum Computing and the University of Waterloo in Waterloo, Canada achieved the first demonstration of quantum key distribution from a ground transmitter to a moving aircraft. They reported optical links with distances between 3–10 km and generated secure keys up to 868 kilobytes in length. Also in June 2017, as part of the Quantum Experiments at Space Scale project, Chinese physicists led by Pan Jianwei at
12975-503: The Lamb shift . Coulomb's law and the electric potential in vacuum near an electric charge are modified. Theoretically, in QCD multiple vacuum states can coexist. The starting and ending of cosmological inflation is thought to have arisen from transitions between different vacuum states. For theories obtained by quantization of a classical theory, each stationary point of the energy in
13148-630: The Rényi entropy and the Tsallis entropy (generalizations of the concept of entropy), differential entropy (a generalization of quantities of information to continuous distributions), and the conditional mutual information . Also, pragmatic information has been proposed as a measure of how much information has been used in making a decision. Coding theory is one of the most important and direct applications of information theory. It can be subdivided into source coding theory and channel coding theory. Using
13321-453: The Sun and the dynamic pressure of the solar winds , so the definition of pressure becomes difficult to interpret. The thermosphere in this range has large gradients of pressure, temperature and composition, and varies greatly due to space weather . Astrophysicists prefer to use number density to describe these environments, in units of particles per cubic centimetre. But although it meets
13494-416: The University of Science and Technology of China measured entangled photons over a distance of 1203 km between two ground stations, laying the groundwork for future intercontinental quantum key distribution experiments. Photons were sent from one ground station to the satellite they had named Micius and back down to another ground station, where they "observed a survival of two-photon entanglement and
13667-431: The condenser is an important aspect of the efficient operation of steam turbines . A steam jet ejector or liquid ring vacuum pump is used for this purpose. The typical vacuum maintained in the condenser steam space at the exhaust of the turbine (also called condenser backpressure) is in the range 5 to 15 kPa (absolute), depending on the type of condenser and the ambient conditions. Evaporation and sublimation into
13840-541: The configuration space gives rise to a single vacuum. String theory is believed to have a huge number of vacua – the so-called string theory landscape . Outer space has very low density and pressure, and is the closest physical approximation of a perfect vacuum. But no vacuum is truly perfect, not even in interstellar space, where there are still a few hydrogen atoms per cubic meter. Stars, planets, and moons keep their atmospheres by gravitational attraction, and as such, atmospheres have no clearly delineated boundary:
14013-605: The log is in base 2. In this way, the extent to which Bob's prior is "wrong" can be quantified in terms of how "unnecessarily surprised" it is expected to make him. Directed information , I ( X n → Y n ) {\displaystyle I(X^{n}\to Y^{n})} , is an information theory measure that quantifies the information flow from the random process X n = { X 1 , X 2 , … , X n } {\displaystyle X^{n}=\{X_{1},X_{2},\dots ,X_{n}\}} to
14186-458: The magnetic field or H -field H to the magnetic induction or B -field B . Here r is a spatial location and t is time. In quantum mechanics and quantum field theory , the vacuum is defined as the state (that is, the solution to the equations of the theory) with the lowest possible energy (the ground state of the Hilbert space ). In quantum electrodynamics this vacuum
14359-472: The parity of those blocks compared. If a difference in parity is found then a binary search is performed to find and correct the error. If an error is found in a block from a previous round that had correct parity then another error must be contained in that block; this error is found and corrected as before. This process is repeated recursively, which is the source of the cascade name. After all blocks have been compared, Alice and Bob both reorder their keys in
14532-431: The pneuma of Stoic physics , aether came to be regarded as the rarefied air from which it took its name, (see Aether (mythology) ). Early theories of light posited a ubiquitous terrestrial and celestial medium through which light propagated. Additionally, the concept informed Isaac Newton 's explanations of both refraction and of radiant heat. 19th century experiments into this luminiferous aether attempted to detect
14705-473: The probability mass function of each source symbol to be communicated, the Shannon entropy H , in units of bits (per symbol), is given by where p i is the probability of occurrence of the i -th possible value of the source symbol. This equation gives the entropy in the units of "bits" (per symbol) because it uses a logarithm of base 2, and this base-2 measure of entropy has sometimes been called
14878-406: The shannon in his honor. Entropy is also commonly computed using the natural logarithm (base e , where e is Euler's number), which produces a measurement of entropy in nats per symbol and sometimes simplifies the analysis by avoiding the need to include extra constants in the formulas. Other bases are also possible, but less commonly used. For example, a logarithm of base 2 = 256 will produce
15051-481: The unit ban . The landmark event establishing the discipline of information theory and bringing it to immediate worldwide attention was the publication of Claude E. Shannon's classic paper "A Mathematical Theory of Communication" in the Bell System Technical Journal in July and October 1948. Historian James Gleick rated the paper as the most important development of 1948, noting that
15224-484: The 1 atm inside the submarine would not normally be considered a vacuum. Therefore, to properly understand the following discussions of vacuum measurement, it is important that the reader assumes the relative measurements are being done on Earth at sea level, at exactly 1 atmosphere of ambient atmospheric pressure. The SI unit of pressure is the pascal (symbol Pa), but vacuum is often measured in torrs , named for an Italian physicist Torricelli (1608–1647). A torr
15397-410: The 17th century. This idea, influenced by Stoic physics , helped to segregate natural and theological concerns. Almost two thousand years after Plato, René Descartes also proposed a geometrically based alternative theory of atomism, without the problematic nothing–everything dichotomy of void and atom. Although Descartes agreed with the contemporary position, that a vacuum does not occur in nature,
15570-440: The 4 different polarization states, as they are not all orthogonal. The only possible measurement is between any two orthogonal states (an orthonormal basis). So, for example, measuring in the rectilinear basis gives a result of horizontal or vertical. If the photon was created as horizontal or vertical (as a rectilinear eigenstate ) then this measures the correct state, but if it was created as 45° or 135° (diagonal eigenstates) then
15743-611: The BB84 protocol. They presented that in DIQKD, the quantum device, which they refer to as the photon source, be manufactured to come with tests that can be run by Alice and Bob to "self-check" if their device is working properly. Such a test would only need to consider the classical inputs and outputs in order to determine how much information is at risk of being intercepted by Eve. A self checking, or "ideal" source would not have to be characterized, and would therefore not be susceptible to implementation flaws. Recent research has proposed using
15916-536: The MFP of room temperature air is roughly 100 mm, which is on the order of everyday objects such as vacuum tubes . The Crookes radiometer turns when the MFP is larger than the size of the vanes. Vacuum quality is subdivided into ranges according to the technology required to achieve it or measure it. These ranges were defined in ISO 3529-1:2019 as shown in the following table (100 Pa corresponds to 0.75 Torr; Torr
16089-452: The UK but, except on heritage railways , they have been replaced by air brakes . Manifold vacuum can be used to drive accessories on automobiles . The best known application is the vacuum servo , used to provide power assistance for the brakes . Obsolete applications include vacuum-driven windscreen wipers and Autovac fuel pumps. Some aircraft instruments ( Attitude Indicator (AI) and
16262-424: The absolute pressure is equal to the current atmospheric pressure. In other words, most low vacuum gauges that read, for example 50.79 Torr. Many inexpensive low vacuum gauges have a margin of error and may report a vacuum of 0 Torr but in practice this generally requires a two-stage rotary vane or other medium type of vacuum pump to go much beyond (lower than) 1 torr. Many devices are used to measure
16435-407: The addition of physically secured relay nodes, which can be placed along the quantum link with the intention of dividing it up into several low-loss sections. Researchers have also recommended the use of quantum repeaters, which when added to the relay nodes make it so that they no longer need to be physically secured. Quantum repeaters, however, are difficult to create and have yet to be implemented on
16608-416: The analysis of music , art creation , imaging system design, study of outer space , the dimensionality of space , and epistemology . Information theory studies the transmission, processing, extraction, and utilization of information . Abstractly, information can be thought of as the resolution of uncertainty. In the case of communication of information over a noisy channel, this abstract concept
16781-480: The assertion: With it came the ideas of: Information theory is based on probability theory and statistics, where quantified information is usually described in terms of bits. Information theory often concerns itself with measures of information of the distributions associated with random variables. One of the most important measures is called entropy , which forms the building block of many other measures. Entropy allows quantification of measure of information in
16954-640: The backbone network through a trusted relay. Launched in August 2016, the QUESS space mission created an international QKD channel between China and the Institute for Quantum Optics and Quantum Information in Vienna , Austria − a ground distance of 7,500 km (4,700 mi), enabling the first intercontinental secure quantum video call. By October 2017, a 2,000-km fiber line was operational between Beijing , Jinan , Hefei and Shanghai . Together they constitute
17127-503: The bell state measurement (BSM) setup. The photons are projected onto a |ψ state, indicating maximum entanglement. The rest of the key exchange protocol used is similar to the original QKD protocol, with the only difference being that keys are generated with two measurement settings instead of one. Since the proposal of Twin Field Quantum Key Distribution in 2018, a myriad of experiments have been performed with
17300-483: The case, then Alice and Bob can conclude Eve has introduced local realism to the system, violating Bell's theorem . If the protocol is successful, the first group can be used to generate keys since those photons are completely anti-aligned between Alice and Bob. In traditional QKD, the quantum devices used must be perfectly calibrated, trustworthy, and working exactly as they are expected to. Deviations from expected measurements can be extremely hard to detect, which leaves
17473-484: The channel capacity. These codes can be roughly subdivided into data compression (source coding) and error-correction (channel coding) techniques. In the latter case, it took many years to find the methods Shannon's work proved were possible. A third class of information theory codes are cryptographic algorithms (both codes and ciphers ). Concepts, methods and results from coding theory and information theory are widely used in cryptography and cryptanalysis , such as
17646-447: The communication. Quantum based security against eavesdropping was validated for the deployed system at over 12 km (7.5 mi) range and 10 dB attenuation over fibre optic channel. A continuous wave laser source was used to generate photons without depolarization effect and timing accuracy employed in the setup was of the order of picoseconds. The Single photon avalanche detector (SPAD) recorded arrival of photons and key rate
17819-505: The computational difficulty of certain mathematical functions , and cannot provide any mathematical proof as to the actual complexity of reversing the one-way functions used. QKD has provable security based on information theory , and forward secrecy . The main drawback of quantum-key distribution is that it usually relies on having an authenticated classical channel of communication. In modern cryptography, having an authenticated classical channel means that one already has exchanged either
17992-430: The correct photon polarization state as sent by Alice, and resends the correct state to Bob. However, if she chooses incorrectly, the state she measures is random, and the state sent to Bob cannot be the same as the state sent by Alice. If Bob then measures this state in the same basis Alice sent, he too gets a random result—as Eve has sent him a state in the opposite basis—with a 50% chance of an erroneous result (instead of
18165-415: The correct result he would get without the presence of Eve). The table below shows an example of this type of attack. Information theory Information theory is the mathematical study of the quantification , storage , and communication of information . The field was established and put on a firm footing by Claude Shannon in the 1940s, though early contributions were made in the 1920s through
18338-523: The definition of outer space, the atmospheric density within the first few hundred kilometers above the Kármán line is still sufficient to produce significant drag on satellites . Most artificial satellites operate in this region called low Earth orbit and must fire their engines every couple of weeks or a few times a year (depending on solar activity). The drag here is low enough that it could theoretically be overcome by radiation pressure on solar sails ,
18511-417: The denser surrounding material continuum would immediately fill any incipient rarity that might give rise to a void. In his Physics , book IV, Aristotle offered numerous arguments against the void: for example, that motion through a medium which offered no impediment could continue ad infinitum , there being no reason that something would come to rest anywhere in particular. In the medieval Muslim world ,
18684-456: The density of atmospheric gas simply decreases with distance from the object. The Earth's atmospheric pressure drops to about 32 millipascals (4.6 × 10 psi) at 100 kilometres (62 mi) of altitude, the Kármán line , which is a common definition of the boundary with outer space. Beyond this line, isotropic gas pressure rapidly becomes insignificant when compared to radiation pressure from
18857-422: The detectors lit up, at which point they publicly reveal the phases p and γ . This is different from traditional QKD, in which the phases used are never revealed. The quantum key distribution protocols described above provide Alice and Bob with nearly identical shared keys, and also with an estimate of the discrepancy between the keys. These differences can be caused by eavesdropping, but also by imperfections in
19030-536: The divergence from the product of the marginal distributions to the actual joint distribution: Mutual information is closely related to the log-likelihood ratio test in the context of contingency tables and the multinomial distribution and to Pearson's χ test : mutual information can be considered a statistic for assessing independence between a pair of variables, and has a well-specified asymptotic distribution. The Kullback–Leibler divergence (or information divergence , information gain , or relative entropy )
19203-511: The efficiency of the cascade protocol. Privacy amplification is a method for reducing (and effectively eliminating) Eve's partial information about Alice and Bob's key. This partial information could have been gained both by eavesdropping on the quantum channel during key transmission (thus introducing detectable errors), and on the public channel during information reconciliation (where it is assumed Eve gains all possible parity information). Privacy amplification uses Alice and Bob's key to produce
19376-412: The entangled states are perfectly correlated in the sense that if Alice and Bob both measure whether their particles have vertical or horizontal polarizations, they always get the same answer with 100% probability. The same is true if they both measure any other pair of complementary (orthogonal) polarizations. This necessitates that the two distant parties have exact directionality synchronization. However,
19549-443: The entire system vulnerable. A new protocol called device independent QKD (DIQKD) or measurement device independent QKD (MDIQKD) allows for the use of uncharacterized or untrusted devices, and for deviations from expected measurements to be included in the overall system. These deviations will cause the protocol to abort when detected, rather than resulting in incorrect data. DIQKD was first proposed by Mayers and Yao, building off of
19722-490: The entropy, H , of X is defined: (Here, I ( x ) is the self-information , which is the entropy contribution of an individual message, and E X {\displaystyle \mathbb {E} _{X}} is the expected value .) A property of entropy is that it is maximized when all the messages in the message space are equiprobable p ( x ) = 1/ n ; i.e., most unpredictable, in which case H ( X ) = log n . The special case of information entropy for
19895-701: The fabrication of semiconductors and optical coatings , and to surface science . The reduction of convection provides the thermal insulation of thermos bottles . Deep vacuum lowers the boiling point of liquids and promotes low temperature outgassing which is used in freeze drying , adhesive preparation, distillation , metallurgy , and process purging. The electrical properties of vacuum make electron microscopes and vacuum tubes possible, including cathode-ray tubes . Vacuum interrupters are used in electrical switchgear. Vacuum arc processes are industrially important for production of certain grades of steel or high purity materials. The elimination of air friction
20068-454: The first century AD. Following Plato , however, even the abstract concept of a featureless void faced considerable skepticism: it could not be apprehended by the senses, it could not, itself, provide additional explanatory power beyond the physical volume with which it was commensurate and, by definition, it was quite literally nothing at all, which cannot rightly be said to exist. Aristotle believed that no void could occur naturally, because
20241-445: The first laboratory vacuum in 1643, and other experimental techniques were developed as a result of his theories of atmospheric pressure. A Torricellian vacuum is created by filling with mercury a tall glass container closed at one end, and then inverting it in a bowl to contain the mercury (see below). Vacuum became a valuable industrial tool in the 20th century with the introduction of incandescent light bulbs and vacuum tubes , and
20414-465: The first to be invented, and they remain the most widely implemented. The other two families are mainly concerned with overcoming practical limitations of experiments. The two protocols described below both use discrete variable coding. This protocol, known as BB84 after its inventors and year of publication, was originally described using photon polarization states to transmit the information. However, any two pairs of conjugate states can be used for
20587-432: The flexure of the diaphragm, which results in a change in capacitance. These gauges are effective from 10 torr to 10 torr, and beyond. Thermal conductivity gauges rely on the fact that the ability of a gas to conduct heat decreases with pressure. In this type of gauge, a wire filament is heated by running current through it. A thermocouple or Resistance Temperature Detector (RTD) can then be used to measure
20760-426: The gas density decreases, the MFP increases, and when the MFP is longer than the chamber, pump, spacecraft, or other objects present, the continuum assumptions of fluid mechanics do not apply. This vacuum state is called high vacuum , and the study of fluid flows in this regime is called particle gas dynamics. The MFP of air at atmospheric pressure is very short, 70 nm , but at 100 mPa (≈ 10 Torr )
20933-416: The gases being measured. Ionization gauges are used in ultrahigh vacuum. They come in two types: hot cathode and cold cathode. In the hot cathode version an electrically heated filament produces an electron beam. The electrons travel through the gauge and ionize gas molecules around them. The resulting ions are collected at a negative electrode. The current depends on the number of ions, which depends on
21106-416: The given distribution can be reliably compressed. The latter is a property of the joint distribution of two random variables, and is the maximum rate of reliable communication across a noisy channel in the limit of long block lengths, when the channel statistics are determined by the joint distribution. The choice of logarithmic base in the following formulae determines the unit of information entropy that
21279-401: The goal of increasing the distance in a QKD system. The most successful of which was able to distribute key information across a distance of 833.8 km. In 2023, Scientists at Indian Institute of Technology (IIT) Delhi have achieved a trusted-node-free quantum key distribution (QKD) up to 380 km in standard telecom fiber with a very low quantum bit error rate (QBER). Many companies around
21452-490: The hemispheres, teams of horses could not separate two hemispheres from which the air had been partially evacuated. Robert Boyle improved Guericke's design and with the help of Robert Hooke further developed vacuum pump technology. Thereafter, research into the partial vacuum lapsed until 1850 when August Toepler invented the Toepler pump and in 1855 when Heinrich Geissler invented the mercury displacement pump, achieving
21625-409: The hub receives quantum messages. To communicate, each node sends a one-time pad to the hub, which it then uses to communicate securely over a classical link. The hub can route this message to another node using another one time pad from the second node. The entire network is secure only if the central hub is secure. Individual nodes require little more than a laser: Prototype nodes are around the size of
21798-487: The important contributions by Rolf Landauer in the 1960s, are explored in Entropy in thermodynamics and information theory . In Shannon's revolutionary and groundbreaking paper, the work for which had been substantially completed at Bell Labs by the end of 1944, Shannon for the first time introduced the qualitative and quantitative model of communication as a statistical process underlying information theory, opening with
21971-454: The initially planned duration of the test. In May 2009, a hierarchical quantum network was demonstrated in Wuhu , China . The hierarchical network consisted of a backbone network of four nodes connecting a number of subnets. The backbone nodes were connected through an optical switching quantum router. Nodes within each subnet were also connected through an optical switch, which were connected to
22144-710: The key and try again, possibly with a different quantum channel, as the security of the key cannot be guaranteed. p {\displaystyle p} is chosen so that if the number of bits known to Eve is less than this, privacy amplification can be used to reduce Eve's knowledge of the key to an arbitrarily small amount at the cost of reducing the length of the key. Artur Ekert 's scheme uses entangled pairs of photons. These can be created by Alice, by Bob, or by some source separate from both of them, including eavesdropper Eve. The photons are distributed so that Alice and Bob each end up with one photon from each pair. The scheme relies on two properties of entanglement. First,
22317-403: The limit of many channel uses, the rate of information that is asymptotically achievable is equal to the channel capacity, a quantity dependent merely on the statistics of the channel over which the messages are sent. Coding theory is concerned with finding explicit methods, called codes , for increasing the efficiency and reducing the error rate of data communication over noisy channels to near
22490-601: The longest running project for testing Quantum Key Distribution (QKD) in a field environment. The main goal of the SwissQuantum network project installed in the Geneva metropolitan area in March 2009, was to validate the reliability and robustness of QKD in continuous operation over a long time period in a field environment. The quantum layer operated for nearly 2 years until the project was shut down in January 2011 shortly after
22663-529: The original state (see No-cloning theorem ). BB84 uses two pairs of states, with each pair conjugate to the other pair, and the two states within a pair orthogonal to each other. Pairs of orthogonal states are referred to as a basis . The usual polarization state pairs used are either the rectilinear basis of vertical (0°) and horizontal (90°), the diagonal basis of 45° and 135° or the circular basis of left- and right-handedness. Any two of these bases are conjugate to each other, and so any two can be used in
22836-766: The outcome of a fair coin flip (which has two equally likely outcomes) provides less information (lower entropy, less uncertainty) than identifying the outcome from a roll of a die (which has six equally likely outcomes). Some other important measures in information theory are mutual information , channel capacity , error exponents , and relative entropy . Important sub-fields of information theory include source coding , algorithmic complexity theory , algorithmic information theory and information-theoretic security . Applications of fundamental topics of information theory include source coding/ data compression (e.g. for ZIP files ), and channel coding/ error detection and correction (e.g. for DSL ). Its impact has been crucial to
23009-576: The paper was "even more profound and more fundamental" than the transistor . He came to be known as the "father of information theory". Shannon outlined some of his initial ideas of information theory as early as 1939 in a letter to Vannevar Bush . Prior to this paper, limited information-theoretic ideas had been developed at Bell Labs , all implicitly assuming events of equal probability. Harry Nyquist 's 1924 paper, Certain Factors Affecting Telegraph Speed , contains
23182-484: The particular results are completely random; it is impossible for Alice to predict if she (and thus Bob) will get vertical polarization or horizontal polarization. Second, any attempt at eavesdropping by Eve destroys these correlations in a way that Alice and Bob can detect. Similarly to BB84 , the protocol involves a private measurement protocol before detecting the presence of Eve. The measurement stage involves Alice measuring each photon she receives using some basis from
23355-413: The physicist and Islamic scholar Al-Farabi wrote a treatise rejecting the existence of the vacuum in the 10th century. He concluded that air's volume can expand to fill available space, and therefore the concept of a perfect vacuum was incoherent. According to Ahmad Dallal , Abū Rayhān al-Bīrūnī states that "there is no observable evidence that rules out the possibility of vacuum". The suction pump
23528-413: The port was sealed. The 17th century saw the first attempts to quantify measurements of partial vacuum. Evangelista Torricelli 's mercury barometer of 1643 and Blaise Pascal 's experiments both demonstrated a partial vacuum. In 1654, Otto von Guericke invented the first vacuum pump and conducted his famous Magdeburg hemispheres experiment, showing that, owing to atmospheric pressure outside
23701-433: The position of a chess piece— X the row and Y the column, then the joint entropy of the row of the piece and the column of the piece will be the entropy of the position of the piece. Despite similar notation, joint entropy should not be confused with cross-entropy . The conditional entropy or conditional uncertainty of X given random variable Y (also called the equivocation of X about Y )
23874-486: The presence of an eavesdropper, Alice and Bob now compare a predetermined subset of their remaining bit strings. If a third party (usually referred to as Eve, for "eavesdropper") has gained any information about the photons' polarization, this introduces errors in Bob's measurements. Other environmental conditions can cause errors in a similar fashion. If more than p {\displaystyle p} bits differ they abort
24047-429: The pressure in a vacuum, depending on what range of vacuum is needed. Hydrostatic gauges (such as the mercury column manometer ) consist of a vertical column of liquid in a tube whose ends are exposed to different pressures. The column will rise or fall until its weight is in equilibrium with the pressure differential between the two ends of the tube. The simplest design is a closed-end U-shaped tube, one side of which
24220-631: The pressure in the gauge. Hot cathode gauges are accurate from 10 torr to 10 torr. The principle behind cold cathode version is the same, except that electrons are produced in a discharge created by a high voltage electrical discharge. Cold cathode gauges are accurate from 10 torr to 10 torr. Ionization gauge calibration is very sensitive to construction geometry, chemical composition of gases being measured, corrosion and surface deposits. Their calibration can be invalidated by activation at atmospheric pressure or low vacuum. The composition of gases at high vacuums will usually be unpredictable, so
24393-407: The protocol, and many optical-fibre -based implementations described as BB84 use phase encoded states. The sender (traditionally referred to as Alice ) and the receiver (Bob) are connected by a quantum communication channel which allows quantum states to be transmitted. In the case of photons this channel is generally either an optical fibre or simply free space . In addition they communicate via
24566-411: The protocol. Below the rectilinear and diagonal bases are used. The first step in BB84 is quantum transmission. Alice creates a random bit (0 or 1) and then randomly selects one of her two bases (rectilinear or diagonal in this case) to transmit it in. She then prepares a photon polarization state depending both on the bit value and basis, as shown in the adjacent table. So for example a 0 is encoded in
24739-499: The quantum device is functioning, this time at a much larger distance of about 400m, using an optical fiber 700m long. The set up for the experiment was similar to the one in the paragraph above, with some key differences. Entanglement was generated in a quantum network link (QNL) between two Rb atoms in separate laboratories located 400m apart, connected by the 700m channel. The atoms are entangled by electronic excitation, at which point two photons are generated and collected, to be sent to
24912-450: The random process Y n = { Y 1 , Y 2 , … , Y n } {\displaystyle Y^{n}=\{Y_{1},Y_{2},\dots ,Y_{n}\}} . The term directed information was coined by James Massey and is defined as where I ( X i ; Y i | Y i − 1 ) {\displaystyle I(X^{i};Y_{i}|Y^{i-1})}
25085-458: The rectilinear basis (+) as a vertical polarization state, and a 1 is encoded in the diagonal basis (x) as a 135° state. Alice then transmits a single photon in the state specified to Bob, using the quantum channel. This process is then repeated from the random bit stage, with Alice recording the state, basis and time of each photon sent. According to quantum mechanics (particularly quantum indeterminacy), no possible measurement distinguishes between
25258-466: The rectilinear measurement instead returns either horizontal or vertical at random. Furthermore, after this measurement the photon is polarized in the state it was measured in (horizontal or vertical), with all information about its initial polarization lost. As Bob does not know the basis the photons were encoded in, all he can do is to select a basis at random to measure in, either rectilinear or diagonal. He does this for each photon he receives, recording
25431-518: The same basis by Alice and Bob while the second contains all other photons. To detect eavesdropping, they can compute the test statistic S {\displaystyle S} using the correlation coefficients between Alice's bases and Bob's similar to that shown in the Bell test experiments . Maximally entangled photons would result in | S | = 2 2 {\displaystyle |S|=2{\sqrt {2}}} . If this were not
25604-542: The same random way, and a new round begins. At the end of multiple rounds Alice and Bob have identical keys with high probability; however, Eve has additional information about the key from the parity information exchanged. However, from a coding theory point of view information reconciliation is essentially source coding with side information. In consequence any coding scheme that works for this problem can be used for information reconciliation. Lately turbocodes, LDPC codes and polar codes have been used for this purpose improving
25777-492: The set Z 0 , Z π 8 , Z π 4 {\displaystyle Z_{0},Z_{\frac {\pi }{8}},Z_{\frac {\pi }{4}}} while Bob chooses from Z 0 , Z π 8 , Z − π 8 {\displaystyle Z_{0},Z_{\frac {\pi }{8}},Z_{-{\frac {\pi }{8}}}} where Z θ {\displaystyle Z_{\theta }}
25950-417: The situation where one transmitting user wishes to communicate to one receiving user. In scenarios with more than one transmitter (the multiple-access channel), more than one receiver (the broadcast channel ) or intermediary "helpers" (the relay channel ), or more general networks , compression followed by transmission may no longer be optimal. Any process that generates successive messages can be considered
26123-406: The success of his namesake coordinate system and more implicitly, the spatial–corporeal component of his metaphysics would come to define the philosophically modern notion of empty space as a quantified extension of volume. By the ancient definition however, directional information and magnitude were conceptually distinct. Medieval thought experiments into the idea of a vacuum considered whether
26296-747: The success of the Voyager missions to deep space, the invention of the compact disc , the feasibility of mobile phones and the development of the Internet and artificial intelligence . The theory has also found applications in other areas, including statistical inference , cryptography , neurobiology , perception , signal processing , linguistics , the evolution and function of molecular codes ( bioinformatics ), thermal physics , molecular dynamics , black holes , quantum computing , information retrieval , intelligence gathering , plagiarism detection , pattern recognition , anomaly detection ,
26469-439: The system, so that a high quality vacuum is one with very little matter left in it. Vacuum is primarily measured by its absolute pressure , but a complete characterization requires further parameters, such as temperature and chemical composition. One of the most important parameters is the mean free path (MFP) of residual gases, which indicates the average distance that molecules will travel between collisions with each other. As
26642-408: The system. Fluids cannot generally be pulled, so a vacuum cannot be created by suction . Suction can spread and dilute a vacuum by letting a higher pressure push fluids into it, but the vacuum has to be created first before suction can occur. The easiest way to create an artificial vacuum is to expand the volume of a container. For example, the diaphragm muscle expands the chest cavity, which causes
26815-455: The temperature of the filament. This temperature is dependent on the rate at which the filament loses heat to the surrounding gas, and therefore on the thermal conductivity. A common variant is the Pirani gauge which uses a single platinum filament as both the heated element and RTD. These gauges are accurate from 10 torr to 10 torr, but they are sensitive to the chemical composition of
26988-409: The time, measurement basis used and measurement result. After Bob has measured all the photons, he communicates with Alice over the public classical channel. Alice broadcasts the basis each photon was sent in, and Bob the basis each was measured in. They both discard photon measurements (bits) where Bob used a different basis, which is half on average, leaving half the bits as a shared key. To check for
27161-585: The transmission line and detectors. As it is impossible to distinguish between these two types of errors, guaranteed security requires the assumption that all errors are due to eavesdropping. Provided the error rate between the keys is lower than a certain threshold (27.6% as of 2002), two steps can be performed to first remove the erroneous bits and then reduce Eve's knowledge of the key to an arbitrary small value. These two steps are known as information reconciliation and privacy amplification respectively, and were first described in 1988. Information reconciliation
27334-460: The true distribution p ( x ) {\displaystyle p(x)} , while Bob believes (has a prior ) that the distribution is q ( x ) {\displaystyle q(x)} , then Bob will be more surprised than Alice, on average, upon seeing the value of X . The KL divergence is the (objective) expected value of Bob's (subjective) surprisal minus Alice's surprisal, measured in bits if
27507-431: The vacuum in the steam space of the condenser, that is, the exhaust of the last stage of the turbine. Mechanical or elastic gauges depend on a Bourdon tube, diaphragm, or capsule, usually made of metal, which will change shape in response to the pressure of the region in question. A variation on this idea is the capacitance manometer , in which the diaphragm makes up a part of a capacitor. A change in pressure leads to
27680-450: The violation of the Bell inequalities. In 2008, exchange of secure keys at 1 Mbit/s (over 20 km of optical fibre) and 10 kbit/s (over 100 km of fibre), was achieved by a collaboration between the University of Cambridge and Toshiba using the BB84 protocol with decoy state pulses. In 2007, Los Alamos National Laboratory / NIST achieved quantum key distribution over
27853-443: The vowel u . Historically, there has been much dispute over whether such a thing as a vacuum can exist. Ancient Greek philosophers debated the existence of a vacuum, or void, in the context of atomism , which posited void and atom as the fundamental explanatory elements of physics. Lucretius argued for the existence of vacuum in the first century BC and Hero of Alexandria tried unsuccessfully to create an artificial vacuum in
28026-425: The word information as a measurable quantity, reflecting the receiver's ability to distinguish one sequence of symbols from any other, thus quantifying information as H = log S = n log S , where S was the number of possible symbols, and n the number of symbols in a transmission. The unit of information was therefore the decimal digit , which since has sometimes been called the hartley in his honor as
28199-417: The works of Harry Nyquist and Ralph Hartley . It is at the intersection of electronic engineering , mathematics , statistics , computer science , neurobiology , physics , and electrical engineering . A key measure in information theory is entropy . Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process . For example, identifying
28372-500: The world offer commercial quantum key distribution, for example: ID Quantique (Geneva), MagiQ Technologies, Inc. (New York), QNu Labs ( Bengaluru , India ), QuintessenceLabs (Australia), QRate (Russia), SeQureNet (Paris), Quantum Optics Jena (Germany) and KEEQuant (Germany). Several other companies also have active research programs, including KETS Quantum Security (UK), Toshiba, HP , IBM , Mitsubishi , NEC and NTT (See External links for direct research links). In 2004,
28545-706: The world's first bank transfer using quantum key distribution was carried out in Vienna , Austria . Quantum encryption technology provided by the Swiss company Id Quantique was used in the Swiss canton (state) of Geneva to transmit ballot results to the capital in the national election occurring on 21 October 2007. In 2013, Battelle Memorial Institute installed a QKD system built by ID Quantique between their main campus in Columbus, Ohio and their manufacturing facility in nearby Dublin. Field tests of Tokyo QKD network have been underway for some time. The DARPA Quantum Network ,
28718-593: The world's first space-ground quantum network. Up to 10 Micius/QUESS satellites are expected, allowing a European–Asian quantum-encrypted network by 2020, and a global network by 2030. The Tokyo QKD Network was inaugurated on the first day of the UQCC2010 conference. The network involves an international collaboration between 7 partners; NEC , Mitsubishi Electric , NTT and NICT from Japan, and participation from Europe by Toshiba Research Europe Ltd. (UK), Id Quantique (Switzerland) and All Vienna (Austria). "All Vienna"
28891-720: Was a 10-node quantum key distribution network, which ran continuously for four years, 24 hours a day, from 2004 to 2007 in Massachusetts in the United States. It was developed by BBN Technologies , Harvard University , Boston University , with collaboration from IBM Research , the National Institute of Standards and Technology , and QinetiQ . It supported a standards-based Internet computer network protected by quantum key distribution. The world's first computer network protected by quantum key distribution
29064-401: Was achieved by University of Geneva and Corning Inc. In the same experiment, a secret key rate of 12.7 kbit/s was generated, making it the highest bit rate system over distances of 100 km. In 2016 a team from Corning and various institutions in China achieved a distance of 404 km, but at a bit rate too slow to be practical. In June 2017, physicists led by Thomas Jennewein at
29237-422: Was achieved in the range of kbps with low Quantum bit error rate. In March 2021, Indian Space Research Organisation also demonstrated a free-space Quantum Communication over a distance of 300 meters. A free-space QKD was demonstrated at Space Applications Centre (SAC), Ahmedabad, between two line-of-sight buildings within the campus for video conferencing by quantum-key encrypted signals. The experiment utilised
29410-500: Was described by Arab engineer Al-Jazari in the 13th century, and later appeared in Europe from the 15th century. European scholars such as Roger Bacon , Blasius of Parma and Walter Burley in the 13th and 14th century focused considerable attention on issues concerning the concept of a vacuum. The commonly held view that nature abhorred a vacuum was called horror vacui . There was even speculation that even God could not create
29583-461: Was discarded. Later, in 1930, Paul Dirac proposed a model of the vacuum as an infinite sea of particles possessing negative energy, called the Dirac sea . This theory helped refine the predictions of his earlier formulated Dirac equation , and successfully predicted the existence of the positron , confirmed two years later. Werner Heisenberg 's uncertainty principle , formulated in 1927, predicted
29756-419: Was formalized in 1948 by Claude Shannon in a paper entitled A Mathematical Theory of Communication , in which information is thought of as a set of possible messages, and the goal is to send these messages over a noisy channel, and to have the receiver reconstruct the message with low probability of error, in spite of the channel noise. Shannon's main result, the noisy-channel coding theorem , showed that, in
29929-565: Was implemented in October 2008, at a scientific conference in Vienna. The name of this network is SECOQC ( Se cure Co mmunication Based on Q uantum C ryptography) and the EU funded this project. The network used 200 km of standard fibre-optic cable to interconnect six locations across Vienna and the town of St Poelten located 69 km to the west. Id Quantique has successfully completed
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