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111-521: The DARPA Quantum Network (2002–2007) was the world's first quantum key distribution (QKD) network, operating 10 optical nodes across Boston and Cambridge, Massachusetts . It became fully operational on October 23, 2003 in BBN's laboratories, and in June 2004 was fielded through dark fiber under the streets of Cambridge and Boston, where it ran continuously for over 3 years. The project also created and fielded

222-509: 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

333-552: 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

444-617: 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)

555-434: 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

666-487: 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

777-645: A Reed-Solomon outer code. The DVB-S2, the DVB-T2 and the DVB-C2 standards all use a BCH code outer code to mop up residual errors after LDPC decoding. 5G NR uses polar code for the control channels and LDPC for the data channels. Although LDPC code has had its success in commercial hard disk drives, to fully exploit its error correction capability in SSDs demands unconventional fine-grained flash memory sensing, leading to an increased memory read latency. LDPC-in-SSD

888-509: 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

999-476: 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

1110-486: 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

1221-535: 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

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1332-573: 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

1443-437: A full suite of industrial-strength QKD protocols based on BB84 . In year 2, BBN created two 'Mark 2' versions of this system (4 nodes) with commercial-quality InGaAs detectors created by IBM Research . These 4 nodes ran continuously in BBN's laboratory from October 2003, then two were deployed at Harvard and Boston University in June 2004, when the network began running continuously across the metro Boston area, 24x7. In year 3,

1554-423: 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

1665-475: 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

1776-416: 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

1887-407: A patent-free alternative of similar performance. Since then, advances in low-density parity-check codes have seen them surpass turbo codes in terms of error floor and performance in the higher code rate range, leaving turbo codes better suited for the lower code rates only. In 2003, an irregular repeat accumulate (IRA) style LDPC code beat six turbo codes to become the error-correcting code in

1998-469: 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

2109-476: 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

2220-420: A single, production-quality protocol stack. Authentication was based on public keys, shared private keys, or a combination of the two. (The shared private keys could be refreshed by QKD-derived keys.) Privacy amplification was implemented via GF[2n] Universal Hash . Entropy estimation was based on Rényi entropy , and implemented by BBBSS 92, Slutsky, Myers / Pearson, and Shor / Preskill protocols. Error correction

2331-430: A sparse parity-check matrix . This sparse matrix is often randomly generated, subject to the sparsity constraints— LDPC code construction is discussed later . These codes were first designed by Robert Gallager in 1960. Below is a graph fragment of an example LDPC code using Forney's factor graph notation . In this graph, n variable nodes in the top of the graph are connected to ( n − k ) constraint nodes in

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2442-434: 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

2553-469: 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,

2664-400: A zero in that position would satisfy the constraint. This procedure is then iterated. The new value for the fourth bit can now be used in conjunction with the first constraint to recover the first bit as seen below. This means that the first bit must be a one to satisfy the leftmost constraint. Thus, the message can be decoded iteratively. For other channel models, the messages passed between

2775-442: 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

2886-558: Is added to row 3. Step 3: Row 2 and 3 are swapped. Step 4: Row 1 is added to row 3. From this, the generator matrix G can be obtained as [ I k | P ] {\displaystyle {\begin{bmatrix}I_{k}|P\end{bmatrix}}} (noting that in the special case of this being a binary code P = − P {\displaystyle P=-P} ), or specifically: Finally, by multiplying all eight possible 3-bit strings by G , all eight valid codewords are obtained. For example,

2997-518: Is an effective approach to deploy LDPC in SSD with a very small latency increase, which turns LDPC in SSD into a reality. Since then, LDPC has been widely adopted in commercial SSDs in both customer-grades and enterprise-grades by major storage venders. Many TLC (and later) SSDs are using LDPC codes. A fast hard-decode (binary erasure) is first attempted, which can fall back into the slower but more powerful soft decoding. LDPC codes functionally are defined by

3108-519: Is iterated until a valid codeword is achieved or decoding is exhausted. This type of decoding is often referred to as sum-product decoding. The decoding of the SPC codes is often referred to as the "check node" processing, and the cross-checking of the variables is often referred to as the "variable-node" processing. In a practical LDPC decoder implementation, sets of SPC codes are decoded in parallel to increase throughput. In contrast, belief propagation on

3219-770: 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

3330-626: 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

3441-581: 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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3552-428: 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

3663-486: 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 ,

3774-429: 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

3885-416: 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

3996-600: The Gilbert–Varshamov bound for linear codes over general fields. Impractical to implement when first developed by Gallager in 1963, LDPC codes were forgotten until his work was rediscovered in 1996. Turbo codes , another class of capacity-approaching codes discovered in 1993, became the coding scheme of choice in the late 1990s, used for applications such as the Deep Space Network and satellite communications . LDPC codes then received renewed interest as

4107-573: 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

4218-564: The Massachusetts Institute of Technology to implement, and experiment with, a proof-of-concept version of the world's first quantum eavesdropper (Eve). When fully built, the network's 10 nodes were as follows. All ran BBN's quantum key distribution and quantum network protocols so they inter-operated to achieve any-to-any key distribution. The DARPA Quantum Network implemented a variety of quantum key distribution protocols, to explore their properties. All were integrated into

4329-417: 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

4440-526: The Unix kernel and field-programmable gate arrays . QKD-derived key material was routinely used for video-conferencing or other applications. The DARPA Quantum Network was built in stages. In the project's first year (year 1), BBN designed and built a full QKD system (Alice and Bob), with an attenuated laser source (~ 0.1 mean photon number) running through telecom fiber, phase-modulated via an actively stabilized Mach-Zender interferometer . BBN also implemented

4551-614: The Wi-Fi 802.11 standard as an optional part of 802.11n and 802.11ac , in the High Throughput (HT) PHY specification. LDPC is a mandatory part of 802.11ax (Wi-Fi 6). Some OFDM systems add an additional outer error correction that fixes the occasional errors (the "error floor") that get past the LDPC correction inner code even at low bit error rates . For example: The Reed-Solomon code with LDPC Coded Modulation (RS-LCM) uses

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4662-416: The binary erasure channel is particularly simple where it consists of iterative constraint satisfaction. For example, consider that the valid codeword, 101011, from the example above, is transmitted across a binary erasure channel and received with the first and fourth bit erased to yield ?01?11. Since the transmitted message must have satisfied the code constraints, the message can be represented by writing

4773-471: The binary symmetric channel is an NP-complete problem, shown by reduction from 3-dimensional matching . So assuming P != NP , which is widely believed, then performing optimal decoding for an arbitrary code of any useful size is not practical. However, sub-optimal techniques based on iterative belief propagation decoding give excellent results and can be practically implemented. The sub-optimal decoding techniques view each parity check that makes up

4884-664: The bipartite graph ). LDPC codes are capacity-approaching codes , which means that practical constructions exist that allow the noise threshold to be set very close to the theoretical maximum (the Shannon limit ) for a symmetric memoryless channel. The noise threshold defines an upper bound for the channel noise, up to which the probability of lost information can be made as small as desired. Using iterative belief propagation techniques, LDPC codes can be decoded in time linear in their block length. LDPC codes are also known as Gallager codes , in honor of Robert G. Gallager , who developed

4995-550: The forward error correction (FEC) system for the ITU-T G.hn standard. G.hn chose LDPC codes over turbo codes because of their lower decoding complexity (especially when operating at data rates close to 1.0 Gbit/s) and because the proposed turbo codes exhibited a significant error floor at the desired range of operation. LDPC codes are also used for 10GBASE-T Ethernet, which sends data at 10 gigabits per second over twisted-pair cables. As of 2009, LDPC codes are also part of

5106-472: 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

5217-440: 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

5328-614: 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

5439-580: The DVB-S2 rate 2/3 code the encoded block size is 64800 symbols (N=64800) with 43200 data bits (K=43200) and 21600 parity bits (M=21600). Each constituent code (check node) encodes 16 data bits except for the first parity bit which encodes 8 data bits. The first 4680 data bits are repeated 13 times (used in 13 parity codes), while the remaining data bits are used in 3 parity codes (irregular LDPC code). For comparison, classic turbo codes typically use two constituent codes configured in parallel, each of which encodes

5550-438: The LDPC as an independent single parity check (SPC) code. Each SPC code is decoded separately using soft-in-soft-out (SISO) techniques such as SOVA , BCJR , MAP , and other derivates thereof. The soft decision information from each SISO decoding is cross-checked and updated with other redundant SPC decodings of the same information bit. Each SPC code is then decoded again using the updated soft decision information. This process

5661-546: The LDPC concept in his doctoral dissertation at the Massachusetts Institute of Technology in 1960. However, LDPC codes require computationally expensive iterative decoding, so they went unused for decades. In 1993 the newly invented turbo codes demonstrated that codes with iterative decoding could far outperform other codes used at that time, but turbo codes were patented and required a fee for use. This raised renewed interest in LDPC codes, which were shown to have similar performance, but were much older and patent-free. Now that

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5772-408: 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

5883-645: 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

5994-505: 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

6105-547: The bottom of the graph. This is a popular way of graphically representing an ( n ,  k ) LDPC code. The bits of a valid message, when placed on the T's at the top of the graph, satisfy the graphical constraints. Specifically, all lines connecting to a variable node (box with an '=' sign) have the same value, and all values connecting to a factor node (box with a '+' sign) must sum, modulo two, to zero (in other words, they must sum to an even number; or there must be an even number of odd values). Ignoring any lines going out of

6216-484: 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

6327-411: The codeword for the bit-string '101' is obtained by: where ⊙ {\displaystyle \odot } is symbol of mod 2 multiplication. As a check, the row space of G is orthogonal to H such that G ⊙ H T = 0 {\displaystyle G\odot H^{T}=0} The bit-string '101' is found in as the first 3 bits of the codeword '101011'. During

6438-447: 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

6549-506: 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

6660-430: 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

6771-416: The correct result he would get without the presence of Eve). The table below shows an example of this type of attack. Low-density parity-check code In information theory , a low-density parity-check ( LDPC ) code is a linear error correcting code , a method of transmitting a message over a noisy transmission channel. An LDPC code is constructed using a sparse Tanner graph (subclass of

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6882-412: The design of well performing low rate codes is easier for turbo codes. As a practical matter, the hardware that forms the accumulators is reused during the encoding process. That is, once a first set of parity bits are generated and the parity bits stored, the same accumulator hardware is used to generate a next set of parity bits. As with other codes, the maximum likelihood decoding of an LDPC code on

6993-424: 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

7104-511: 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

7215-478: The encoding of a frame, the input data bits (D) are repeated and distributed to a set of constituent encoders. The constituent encoders are typically accumulators and each accumulator is used to generate a parity symbol. A single copy of the original data (S 0,K-1 ) is transmitted with the parity bits (P) to make up the code symbols. The S bits from each constituent encoder are discarded. The parity bit may be used within another constituent code. In an example using

7326-412: 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,

7437-498: The entire input block (K) of data bits. These constituent encoders are recursive convolutional codes (RSC) of moderate depth (8 or 16 states) that are separated by a code interleaver which interleaves one copy of the frame. The LDPC code, in contrast, uses many low depth constituent codes (accumulators) in parallel, each of which encode only a small portion of the input frame. The many constituent codes can be viewed as many low depth (2 state) " convolutional codes " that are connected via

7548-447: 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

7659-402: The first 3 bits of the codeword. While illustrative, this erasure example does not show the use of soft-decision decoding or soft-decision message passing, which is used in virtually all commercial LDPC decoders. In recent years , there has also been a great deal of work spent studying the effects of alternative schedules for variable-node and constraint-node update. The original technique that

7770-466: 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

7881-445: The fundamental patent for turbo codes has expired (on August 29, 2013), LDPC codes are still used for their technical merits. LDPC codes have been shown to have ideal combinatorial properties. In his dissertation, Gallager showed that LDPC codes achieve the Gilbert–Varshamov bound for linear codes over binary fields with high probability. In 2020 it was shown that Gallager's LDPC codes achieve list decoding capacity and also achieve

7992-403: 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

8103-409: 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

8214-454: 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

8325-711: 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,

8436-601: 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

8547-460: The most are the ones that need to be updated first. Highly reliable nodes, whose log-likelihood ratio (LLR) magnitude is large and does not change significantly from one update to the next, do not require updates with the same frequency as other nodes, whose sign and magnitude fluctuate more widely. These scheduling algorithms show greater speed of convergence and lower error floors than those that use flooding. These lower error floors are achieved by

8658-531: The network expanded to 8 nodes with the addition of an entanglement-based system (derived from work at Boston University ) designed for telecom fibers, and a high-speed atmospheric (freespace) link designed and built by the National Institute of Standards and Technology . In year 4, BBN added a second freespace link to the overall network, using nodes created by Qinetiq , and investigated improved QKD protocols and detectors. Finally, in year 5, BBN added

8769-482: The network to relay materials for key distillation between the two endpoints. This approach permitted nodes to agree upon shared key material even if they were implemented via two incompatible technologies; for example, a node based on phase-modulation through fiber could exchange keys with one based on polarization-modulation through the atmosphere. In fact, it even permitted transmitters to share key material with other (compatible or incompatible) transmitters. Furthermore,

8880-417: The new DVB-S2 standard for digital television . The DVB-S2 selection committee made decoder complexity estimates for the turbo code proposals using a much less efficient serial decoder architecture rather than a parallel decoder architecture. This forced the turbo code proposals to use frame sizes on the order of one half the frame size of the LDPC proposals. In 2008, LDPC beat convolutional turbo codes as

8991-529: 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

9102-484: 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

9213-651: The picture, the parity-check matrix representing this graph fragment is In this matrix, each row represents one of the three parity-check constraints, while each column represents one of the six bits in the received codeword. In this example, the eight codewords can be obtained by putting the parity-check matrix H into this form [ − P T | I n − k ] {\displaystyle {\begin{bmatrix}-P^{T}|I_{n-k}\end{bmatrix}}} through basic row operations in GF(2) : Step 1: H. Step 2: Row 1

9324-438: The picture, there are eight possible six-bit strings corresponding to valid codewords: (i.e., 000000, 011001, 110010, 101011, 111100, 100101, 001110, 010111). This LDPC code fragment represents a three-bit message encoded as six bits. Redundancy is used, here, to increase the chance of recovering from channel errors. This is a (6, 3) linear code , with n  = 6 and k  = 3. Again ignoring lines going out of

9435-486: 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

9546-407: 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

9657-411: 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

9768-501: 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

9879-533: The raw key material could be routed by multiple "striped" paths through the network (e.g. disjoint paths) and recombined end-to-end, thus erasing the advantage that Eve would gain by controlling one of the network nodes along the way. Second, QKD-aware optical routing protocols enabled nodes to control transparent optical switches within the network, so that multiple QKD systems could share the same optical network infrastructure. Quantum key distribution An important and unique property of quantum key distribution

9990-444: The received message on the top of the factor graph. In this example, the first bit cannot yet be recovered, because all of the constraints connected to it have more than one unknown bit. In order to proceed with decoding the message, constraints connecting to only one of the erased bits must be identified. In this example, only the second constraint suffices. Examining the second constraint, the fourth bit must have been zero, since only

10101-458: 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

10212-466: 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

10323-475: The repeat and distribute operations. The repeat and distribute operations perform the function of the interleaver in the turbo code. The ability to more precisely manage the connections of the various constituent codes and the level of redundancy for each input bit give more flexibility in the design of LDPC codes, which can lead to better performance than turbo codes in some instances. Turbo codes still seem to perform better than LDPCs at low code rates, or at least

10434-518: 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

10545-545: 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

10656-492: 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 }}

10767-409: 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

10878-587: 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

10989-459: The variable nodes and check nodes are real numbers , which express probabilities and likelihoods of belief. This result can be validated by multiplying the corrected codeword r by the parity-check matrix H : Because the outcome z (the syndrome ) of this operation is the three × one zero vector, the resulting codeword r is successfully validated. After the decoding is completed, the original message bits '101' can be extracted by looking at

11100-451: 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

11211-500: 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,

11322-486: The world's first superconducting nanowire single-photon detector to the operational network. It was created by a collaboration between researchers at BBN, the University of Rochester , and the National Institute of Standards and Technology; that first 100 MHz system ran 20x faster than any existing single-photon detector at telecom wavelengths. In that final year, BBN also collaborated with researchers at

11433-715: The world's first superconducting nanowire single-photon detector . It was sponsored by DARPA as part of the QuIST program, and built and operated by BBN Technologies in close collaboration with colleagues at Harvard University and the Boston University Photonics Center . The DARPA Quantum Network was fully compatible with standard Internet technology, and could provide QKD-derived key material to create Virtual Private Networks , to support IPsec or other authentication, or for any other purpose. All control mechanisms and protocols were implemented in

11544-710: 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 ,

11655-598: 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"

11766-652: 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

11877-402: 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

11988-423: 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

12099-564: Was implemented by a BBN variant of the Cascade protocol, or the BBN Niagara protocol which provided efficient, one-pass operation near the Shannon limit via forward error correction based on low-density parity-check codes (LDPC). Sifting was performed either by traditional methods, run-length encoding, or so-called "SARG" sifting. It also implemented two major forms of QKD networking protocols. First, key relay employed "trusted" nodes in

12210-566: 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

12321-435: Was used for decoding LDPC codes was known as flooding . This type of update required that, before updating a variable node, all constraint nodes needed to be updated and vice versa. In later work by Vila Casado et al. , alternative update techniques were studied, in which variable nodes are updated with the newest available check-node information. The intuition behind these algorithms is that variable nodes whose values vary

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