Applications of Quantum Information

This chapter presents some applications of Quantum Information Theory that deviate from the problem of reliably transmitting classical information. In fact, the inherent randomness in quantum measurements lends itself to devising methods for the fast automatic generation of true random numbers with quantum devices. Similarly, the possibility of detecting the presence of a measurement operation on a single quantum system, from another, nonorthogonal measurement on the same system, has opened the way to quantum cryptography. This constitutes an unconditionally secure replacement for the schemes that currently lie at the core of many protocols for securing the transmission and storing of information from a rational attacker. Eventually, we devote a paragraph to the topic of quantum teleportation, that is, the transfer of an unknown quantum state between two different locations that is achieved by making use of entanglement and only transmitting classical information.

[1]  F. Martini,et al.  Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels , 1997, quant-ph/9710013.

[2]  T. Elgamal.  A public key cryptosystem and a signature scheme based on discrete logarithms , 1984, CRYPTO 1984.

[3]  E. Knill,et al.  Complete quantum teleportation using nuclear magnetic resonance , 1998, Nature.

[4]  Paolo Villoresi,et al.  Experimental quantum key distribution with finite-key security analysis for noisy channels , 2013, Nature Communications.

[5]  R. Dong,et al.  A generator for unique quantum random numbers based on vacuum states , 2010 .

[6]  H. Weinfurter,et al.  Experimental quantum teleportation , 1997, Nature.

[7]  G. Vallone,et al.  Loss tolerant device-independent quantum key distribution: a proof of principle , 2013, 1310.6664.

[8]  Jian-Wei Pan,et al.  Quantum teleportation and entanglement distribution over 100-kilometre free-space channels , 2012, Nature.

[9]  T. Symul,et al.  Real time demonstration of high bitrate quantum random number generation with coherent laser light , 2011, 1107.4438.

[10]  David Elkouss,et al.  Information reconciliation for quantum key distribution , 2010, 1007.1616.

[11]  Kimble,et al.  Unconditional quantum teleportation , 1998, Science.

[12]  H. Weinfurter,et al.  High speed optical quantum random number generation. , 2010, Optics express.

[13]  Hoi-Kwong Lo,et al.  Efficient Quantum Key Distribution Scheme and a Proof of Its Unconditional Security , 2004, Journal of Cryptology.

[14]  Seth Lloyd,et al.  Gaussian quantum information , 2011, 1110.3234.

[15]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[16]  Adi Shamir,et al.  A method for obtaining digital signatures and public-key cryptosystems , 1978, CACM.

[17]  Whitfield Diffie,et al.  New Directions in Cryptography , 1976, IEEE Trans. Inf. Theory.

[18]  Ueli Maurer,et al.  Secret key agreement by public discussion from common information , 1993, IEEE Trans. Inf. Theory.

[19]  Charles H. Bennett,et al.  Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. , 1993, Physical review letters.

[20]  G. Marsaglia.  Random numbers fall mainly in the planes. , 1968, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[22]  B. M. Rogina,et al.  Quantum random number generator based on photonic emission in semiconductors. , 2006, The Review of scientific instruments.

[23]  Charles H. Bennett,et al.  Quantum cryptography without Bell's theorem. , 1992, Physical review letters.

[24]  H. Weinfurter,et al.  A fast and compact quantum random number generator , 1999, quant-ph/9912118.

[25]  P. Grangier,et al.  Continuous variable quantum cryptography using coherent states. , 2001, Physical review letters.

[26]  Ueli Maurer,et al.  Generalized privacy amplification , 1994, Proceedings of 1994 IEEE International Symposium on Information Theory.

[27]  Xiaosong Ma,et al.  Quantum teleportation over 143 kilometres using active feed-forward , 2012, Nature.

[28]  Marco Tomamichel,et al.  Tight finite-key analysis for quantum cryptography , 2011, Nature Communications.

[29]  Gilles Brassard,et al.  Quantum cryptography: Public key distribution and coin tossing , 2014, Theor. Comput. Sci..

[30]  N. Cerf,et al.  Quantum key distribution using gaussian-modulated coherent states , 2003, Nature.

[31]  Stephen Wiesner,et al.  Conjugate coding , 1983, SIGA.