Quantum key distribution

This protocol, known as BB84 after its inventors and year of publication, was originally described using photon polarization states to transmit the information.[3] However, any two pairs of conjugate states can be used for 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 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.[4][5]

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 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 the protocol. Below the rectilinear and diagonal bases are used.

Basis	0	1

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 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 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 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 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.

Alice's random bit	0	1	1	0	1	0	0	1
Alice's random sending basis
Photon polarization Alice sends
Bob's random measuring basis
Photon polarization Bob measures
PUBLIC DISCUSSION OF BASIS
Shared secret key	0		1			0		1

To check for 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 ${\displaystyle p}$ bits differ they abort the key and try again, possibly with a different quantum channel, as the security of the key cannot be guaranteed. ${\displaystyle p}$ 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[6] 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, 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, 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 the set ${\displaystyle Z_{0},Z_{\frac {\pi }{8}},Z_{\frac {\pi }{4}}}$ while Bob chooses from ${\displaystyle Z_{0},Z_{\frac {\pi }{8}},Z_{-{\frac {\pi }{8}}}}$ where ${\displaystyle Z_{\theta }}$ is the ${\displaystyle \{|{\uparrow }\rangle ,\;|{\rightarrow }\rangle \}}$ basis rotated by ${\displaystyle \theta }$. 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 the same basis by Alice and Bob while the second contains all other photons. To detect eavesdropping, they can compute the test statistic ${\displaystyle S}$ 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 ${\displaystyle |S|=2{\sqrt {2}}}$. If this were not 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 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.[13]

In 2007, Los Alamos National Laboratory/NIST achieved quantum key distribution over a 148.7 km of optic fibre using the BB84 protocol.[14] 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,[15] and using BB84 enhanced with decoy states[16][17][18][19][20] in 2007.[21]

As of August 2015 the longest distance for optical fiber (307 km)[22] 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.[23]

In June 2017, physicists led by Thomas Jennewein at 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.[24]

Also in June 2017, as part of the Quantum Experiments at Space Scale project, Chinese physicists led by Pan Jianwei at 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.[25] 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 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."[26] 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.[27]

In May 2019 a group led by Hong Guo at Peking University and Beijing University of Posts and Telecommunications reported field tests of 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.[28]

There are currently four companies offering commercial quantum key distribution systems; ID Quantique (Geneva), MagiQ Technologies, Inc. (New York), QuintessenceLabs (Australia) and SeQureNet (Paris). Several other companies also have active research programs, including Toshiba, HP, IBM, Mitsubishi, NEC and NTT (See External links for direct research links).

In 2004, the world's first bank transfer using quantum key distribution was carried out in Vienna, Austria.[29] 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.[30] 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.[31] Field tests of Tokyo QKD network have been underway for some time.[32]

The DARPA Quantum Network,[33] 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 was implemented in October 2008, at a scientific conference in Vienna. The name of this network is SECOQC (Secure Communication Based on Quantum Cryptography) 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.[34]

Id Quantique has successfully completed 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 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 though an optical switching quantum router. Nodes within each subnet were also connected though an optical switch, which were connected to the backbone network though a trusted relay.[35]

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.[36][37][38] By October 2017, a 2,000-km fiber line was operational between Beijing, Jinan, Hefei and Shanghai.[39] Together they constitute the world's first space-ground quantum network.[40] Up to 10 Micius/QUESS satellites are expected,[41] allowing a European–Asian quantum-encrypted network by 2020, and a global network by 2030.[42][43]

The Tokyo QKD Network[44] 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" 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 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 a box of matches.[45]

The simplest type of possible attack 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 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 the correct result he would get without the presence of Eve). The table below shows an example of this type of attack.

Alice's random bit	0	1	1	0	1	0	0	1
Alice's random sending basis
Photon polarization Alice sends
Eve's random measuring basis
Polarization Eve measures and sends
Bob's random measuring basis
Photon polarization Bob measures
PUBLIC DISCUSSION OF BASIS
Shared secret key	0		0			0		1
Errors in key	✓		✘			✓		✓

The probability Eve chooses the incorrect basis is 50% (assuming Alice chooses randomly), and if Bob measures this intercepted photon in the basis Alice sent he gets a random result, i.e., an incorrect result with probability of 50%. The probability an intercepted photon generates an error in the key string is then 50% × 50% = 25%. If Alice and Bob publicly compare ${\displaystyle n}$ of their key bits (thus discarding them as key bits, as they are no longer secret) the probability they find disagreement and identify the presence of Eve is

${\displaystyle P_{d}=1-\left({\frac {3}{4}}\right)^{n}}$

So to detect an eavesdropper with probability ${\displaystyle P_{d}=0.999999999}$ Alice and Bob need to compare ${\displaystyle n=72}$ key bits.

Quantum key distribution is vulnerable to a man-in-the-middle attack when used without authentication to the same extent as any classical protocol, since no known principle of quantum mechanics can distinguish friend from foe. As in the classical case, Alice and Bob cannot authenticate each other and establish a secure connection without some means of verifying each other's identities (such as an initial shared secret). If Alice and Bob have an initial shared secret then they can use an unconditionally secure authentication scheme (such as Carter-Wegman,[46]) along with quantum key distribution to exponentially expand this key, using a small amount of the new key to authenticate the next session.[47] Several methods to create this initial shared secret have been proposed, for example using a 3rd party[48] or chaos theory.[49] Nevertheless, only "almost strongly universal" family of hash functions can be used for unconditionally secure authentication.[50]

In the BB84 protocol Alice sends quantum states to Bob using single photons. In practice many implementations use laser pulses attenuated to a very low level to send the quantum states. These laser pulses contain a very small number of photons, for example 0.2 photons per pulse, which are distributed according to a Poisson distribution. This means most pulses actually contain no photons (no pulse is sent), some pulses contain 1 photon (which is desired) and a few pulses contain 2 or more photons. If the pulse contains more than one photon, then Eve can split off the extra photons and transmit the remaining single photon to Bob. This is the basis of the photon number splitting attack,[51] where Eve stores these extra photons in a quantum memory until Bob detects the remaining single photon and Alice reveals the encoding basis. Eve can then measure her photons in the correct basis and obtain information on the key without introducing detectable errors.

Even with the possibility of a PNS attack a secure key can still be generated, as shown in the GLLP security proof;[52] however, a much higher amount of privacy amplification is needed reducing the secure key rate significantly (with PNS the rate scales as ${\displaystyle t^{2}}$ as compared to ${\displaystyle t}$ for a single photon sources, where ${\displaystyle t}$ is the transmittance of the quantum channel).

There are several solutions to this problem. The most obvious is to use a true single photon source instead of an attenuated laser. While such sources are still at a developmental stage QKD has been carried out successfully with them.[53] However, as current sources operate at a low efficiency and frequency key rates and transmission distances are limited. Another solution is to modify the BB84 protocol, as is done for example in the SARG04 protocol,[54] in which the secure key rate scales as ${\displaystyle t^{3/2}}$. The most promising solution is the decoy states[16][17][18][19][20] in which Alice randomly sends some of her laser pulses with a lower average photon number. These decoy states can be used to detect a PNS attack, as Eve has no way to tell which pulses are signal and which decoy. Using this idea the secure key rate scales as ${\displaystyle t}$, the same as for a single photon source. This idea has been implemented successfully first at the University of Toronto,[55][56] and in several follow-up QKD experiments,[57] allowing for high key rates secure against all known attacks.

Because currently a dedicated fibre optic line (or line of sight in free space) is required between the two points linked by quantum key distribution, a denial of service attack can be mounted by simply cutting or blocking the line. This is one of the motivations for the development of quantum key distribution networks, which would route communication via alternate links in case of disruption.

A quantum key distribution system may be probed by Eve by sending in bright light from the quantum channel and analyzing the back-reflections in a Trojan-horse attack. In a recent research study it has been shown that Eve discerns Bob's secret basis choice with higher than 90% probability, breaching the security of the system.[58]

If Eve is assumed to have unlimited resources, for example both classical and quantum computing power, there are many more attacks possible. BB84 has been proven secure against any attacks allowed by quantum mechanics, both for sending information using an ideal photon source which only ever emits a single photon at a time,[59] and also using practical photon sources which sometimes emit multiphoton pulses.[52] These proofs are unconditionally secure in the sense that no conditions are imposed on the resources available to the eavesdropper; however, there are other conditions required:

1. Eve cannot physically access Alice and Bob's encoding and decoding devices.
2. The random number generators used by Alice and Bob must be trusted and truly random (for example a Quantum random number generator).
3. The classical communication channel must be authenticated using an unconditionally secure authentication scheme.
4. The message must be encrypted using one-time pad like scheme