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Quantum Key Distribution

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Definition: methods for the secure distribution of encryption keys

German: Quanten-Schl├╝sselverteilung

Categories: methods, quantum optics

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Quantum key distribution is a technique used in the context of quantum cryptography in order to generate a perfectly random key which is shared by a sender and a recipient while making sure that nobody else has a chance to learn about the key, e.g. by intercepting the communication channel used during the process. Basic principles of quantum mechanics are exploited to ensure that. Only if quantum mechanics were to turn out to be a flawed theory (for which there is no reasonable evidence after decades of intense research), it might be possible to break the security of such a communication system.

The best known and popular scheme of quantum key distribution is based on the Bennet–Brassard protocol (in short: BB84), which was invented in 1984 [1]. It relies on the no-cloning theorem [3, 4] for non-orthogonal quantum states. For example, it can be implemented using polarization states of single photons. Briefly, the Bennet–Brassard protocol works as follows:

A possible eavesdropper (called Eve) would have to detect the photons' polarization directions without knowing the corresponding base states. In those cases where Eve's guess concerning the base states is wrong, Eve obtains random results. If Eve sends out photons with these polarization directions, Bob's results will also be random in cases where Bob's guess was right. This will therefore be detected during the last stage (the bit verification). Quantum mechanics would not allow Eve to do a polarization measurement without projecting the photon state onto the chosen base states, i.e., without altering the photon states.

Note that Alice and Bob actually need to carry out secure authentication in order to prevent an interceptor from manipulating their public communications. This also requires some secret key, which at a first glance would seem to lead to a catch-22 situation: you need a secret key in order to generate another secret key. However, authentication requires only a short key, whereas the quantum key distribution scheme can generate a much longer one and is therefore still useful.

Some remaining problems are:

A modified cryptography scheme was suggested in 1991 by Ekert [2]. Here, entangled states are used instead of the randomly chosen measurement basis. In many respects, this protocol is similar to the BB84 protocol.

Some quantum key distribution systems have been demonstrated which promise unconditional security for transmission distances up to a few tens of kilometers, although at least one system has been proven not to be perfectly secure; successful eavesdropping has been demonstrated [10]. It should be possible, however, to eliminate such security loopholes with more careful implementations. Further system refinements should also allow for transmission distances over 100 km. Research is also directed at developing more practical single-photon and correlated photon pair sources, based on, e.g., spontaneous parametric downconversion in χ(2) crystals or spontaneous four-wave mixing in optical fibers.

There are already some commercial quantum key distribution systems which can be used by banks, for example.

Bibliography

[1]C. H. Bennet and G. Brassard, “Quantum Cryptography: Public key distribution and coin tossing”, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, Bangalore, p. 175 (1984) (Bennet–Brassard protocol)
[2]A. Ekert, “Quantum cryptography based on Bell´s theorem”, Phys. Rev. Lett. 67 (6), 661 (1991)
[3]W. K. Wooters and W. H. Zurek, “A single quantum cannot be cloned”, Nature 299, 802 (1982) (no-cloning theorem)
[4]N. J. Cerf and J. Fiurasek, “Optical quantum cloning – a review”, Prog. Opt. 49, 455 (2006)
[5]A. Tanaka et al., “Ultra fast quantum key distribution over a 97 km installed telecom fiber with wavelength division multiplexing clock synchronization”, Opt. Express 16 (15), 11354 (2008)
[6]C. Erven et al., “Entangled quantum key distribution over two free-space optical links”, Opt. Express 16 (21), 16840 (2008)
[7]A. R. Dixon et al., “Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate”, Opt. Express 16 (23), 18790 (2008)
[8]C. Bonato et al., “Feasibility of satellite quantum key distribution”, New J. Phys. 11, 045017 (2009)
[9]D. Stucki et al., “High rate, long-distance quantum key distribution over 250 km of ultra low loss fibres”, New J. Phys. 11, 075003 (2009)
[10]I. Gerhardt et al., “Full-field implementation of a perfect eavesdropper on a quantum cryptography system”, Nature Commun. 2, 349 (2011), DOI: 10.1038/ncomms1348
[11]H-K. Lo, M. Curty and K. Tamaki, “Secure quantum key distribution” (review paper), Nature Photon. 8, 595 (2014)
[12]Q. Zhang et al., “Large scale quantum key distribution: challenges and solutions”, Opt. Express 26 (18), 24260 (2018)

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See also: quantum cryptography, optical data transmission
and other articles in the categories methods, quantum optics

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