Security proof of quantum key distribution with detection efficiency mismatch

In theory, quantum key distribution (QKD) offers unconditional security based on the laws of physics. However, as demonstrated in recent quantum hacking theory and experimental papers, detection efficiency loophole can be fatal to the security of practical QKD systems. Here, we describe the physical origin of detection efficiency mismatch in various domains including spatial, spectral, and time domains and in various experimental set-ups. More importantly, we prove the unconditional security of QKD even with detection efficiency mismatch. We explicitly show how the key generation rate is characterized by the maximal detection efficiency ratio between the two detectors. Furthermore, we prove that by randomly switching the bit assignments of the detectors, the effect of detection efficiency mismatch can be completely eliminated.

[1]  P. Oscar Boykin,et al.  A Proof of the Security of Quantum Key Distribution , 1999, STOC '00.

[2]  Won-Young Hwang.  Quantum key distribution with high loss: toward global secure communication. , 2003, Physical review letters.

[3]  E. Santos,et al.  Local realism has not been refuted by atomic cascade experiments , 1983 .

[4]  Shor,et al.  Simple proof of security of the BB84 quantum key distribution protocol , 2000, Physical review letters.

[5]  J. M. Ettinger,et al.  Enhancing practical security of quantum key distribution with a few decoy states , 2005, quant-ph/0503002.

[6]  Hoi-Kwong Lo,et al.  Proof of security of quantum key distribution with two-way classical communications , 2001, IEEE Trans. Inf. Theory.

[7]  H. Chau.  Practical scheme to share a secret key through a quantum channel with a 27.6% bit error rate , 2002 .

[8]  R. Renner,et al.  Information-theoretic security proof for quantum-key-distribution protocols , 2005, quant-ph/0502064.

[9]  M. Koashi,et al.  Unconditional security of the Bennett 1992 quantum-key-distribution scheme with a strong reference pulse , 2006, quant-ph/0607082.

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

[11]  H. Lo,et al.  Performance of two quantum-key-distribution protocols , 2006 .

[12]  P. Oscar Boykin,et al.  A Proof of the Security of Quantum Key Distribution , 1999, Symposium on the Theory of Computing.

[13]  H. Weinfurter,et al.  Entanglement-based quantum communication over 144km , 2007 .

[14]  V. Scarani,et al.  Secrecy extraction from no-signaling correlations , 2006, quant-ph/0606197.

[15]  J. Skaar,et al.  Effects of detector efficiency mismatch on security of quantum cryptosystems , 2005, quant-ph/0511032.

[16]  Hoi-Kwong Lo,et al.  Security proof of a three-state quantum-key-distribution protocol without rotational symmetry , 2006 .

[17]  E. Santos,et al.  Bell’s theorem: Local realism versus quantum mechanics , 1990 .

[18]  K. Tamaki,et al.  Security proof for quantum-key-distribution systems with threshold detectors , 2008, 0803.4226.

[19]  Normand J. Beaudry,et al.  Squashing models for optical measurements in quantum communication. , 2008, Physical review letters.

[20]  Gilles Brassard,et al.  Quantum Cryptography , 2005, Encyclopedia of Cryptography and Security.

[21]  R. Renner,et al.  A Generic Security Proof for Quantum Key Distribution , 2004, quant-ph/0402131.

[22]  Stephen P. Boyd,et al.  Semidefinite Programming , 1996, SIAM Rev..

[23]  H. Lo,et al.  Unconditionally secure key distillation from multiphotons , 2004, quant-ph/0412035.

[24]  Christine Chen,et al.  Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems , 2007, 0704.3253.

[25]  Vadim Makarov,et al.  Faked states attack using detector efficiency mismatch on SARG04, phase-time, DPSK, and Ekert protocols , 2007, Quantum Inf. Comput..

[26]  Ivan Damgård,et al.  Experimental quantum key distribution with proven security against realistic attacks , 2001 .

[27]  Robert König,et al.  Universally Composable Privacy Amplification Against Quantum Adversaries , 2004, TCC.

[28]  M. Koashi.  Efficient quantum key distribution with practical sources and detectors , 2006, quant-ph/0609180.

[29]  Xiang-Bin Wang.  A decoy-state protocol for quantum cryptography with 4 intensities of coherent states , 2008 .

[30]  N. Gisin,et al.  Trojan-horse attacks on quantum-key-distribution systems (6 pages) , 2005, quant-ph/0507063.

[31]  H. Weinfurter,et al.  Experimental Demonstration of Free-Space Decoy-State Quantum Key Distribution over 144 km , 2007, 2007 European Conference on Lasers and Electro-Optics and the International Quantum Electronics Conference.

[32]  Michal Horodecki,et al.  General Paradigm for Distilling Classical Key From Quantum States , 2009, IEEE Transactions on Information Theory.

[33]  T. Mor,et al.  Quantum-Space Attacks , 2007, 0711.3019.

[34]  Christian Kurtsiefer,et al.  Free-space quantum key distribution with entangled photons , 2006 .

[35]  Renato Renner,et al.  Security of quantum-key-distribution protocols using two-way classical communication or weak coherent pulses , 2006, quant-ph/0610151.

[36]  Jean B. Lasserre,et al.  Global Optimization with Polynomials and the Problem of Moments , 2000, SIAM J. Optim..

[37]  M. Koashi.  Simple security proof of quantum key distribution via uncertainty principle , 2005, quant-ph/0505108.

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

[39]  Xiongfeng Ma,et al.  ar X iv : q ua ntp h / 05 12 08 0 v 2 1 1 A pr 2 00 6 TIMESHIFT ATTACK IN PRACTICAL QUANTUM , 2005 .

[40]  N. Gisin,et al.  From Bell's theorem to secure quantum key distribution. , 2005, Physical review letters.

[41]  Marius A Albota,et al.  Efficient single-photon counting at 1.55 microm by means of frequency upconversion. , 2004, Optics letters.

[42]  Peterson,et al.  Daylight quantum key distribution over 1.6 km , 2000, Physical review letters.

[43]  Renato Renner.  Information Security in a Quantum World , 2011, MEMICS.

[44]  Lo,et al.  Unconditional security of quantum key distribution over arbitrarily long distances , 1999, Science.

[45]  Yi Zhao,et al.  Experimental quantum key distribution with decoy states. , 2006, Physical review letters.

[46]  Masahito Hayashi.  General theory for decoy-state quantum key distribution with an arbitrary number of intensities , 2007 .

[47]  H. Lo,et al.  Practical Decoy State for Quantum Key Distribution , 2005, quant-ph/0503005.

[48]  Johannes Skaar,et al.  Security of quantum key distribution with bit and basis dependent detector flaws , 2008, Quantum Inf. Comput..

[49]  Jian-Wei Pan,et al.  Experimental free-space distribution of entangled photon pairs over 13 km: towards satellite-based global quantum communication. , 2005, Physical review letters.

[50]  Li Qian,et al.  Simulation and Implementation of Decoy State Quantum Key Distribution over 60km Telecom Fiber , 2006, 2006 IEEE International Symposium on Information Theory.

[51]  Dominic Mayers,et al.  Unconditional security in quantum cryptography , 1998, JACM.

[52]  C. M. Simmons,et al.  Practical free-space quantum key distribution over 1 km , 1998 .

[53]  Sellami Ali,et al.  DECOY STATE QUANTUM KEY DISTRIBUTION , 2010 .

[54]  John Preskill,et al.  Security of quantum key distribution using weak coherent states with nonrandom phases , 2007, Quantum Inf. Comput..

[55]  H. Inamori,et al.  Unconditional security of practical quantum key distribution , 2007 .

[56]  Kazuoki Azuma.  WEIGHTED SUMS OF CERTAIN DEPENDENT RANDOM VARIABLES , 1967 .

[57]  Xiang‐Bin Wang,et al.  Beating the PNS attack in practical quantum cryptography , 2004 .

[58]  Richard J. Hughes,et al.  Practical free-space quantum key distribution over 10 km in daylight and at night , 2002, quant-ph/0206092.

[59]  John Preskill,et al.  Security of quantum key distribution with imperfect devices , 2002, International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings..

[60]  Norbert Lütkenhaus,et al.  Entanglement as a precondition for secure quantum key distribution. , 2004, Physical review letters.

[61]  B Kraus,et al.  Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. , 2004, Physical review letters.

[62]  J-C Boileau,et al.  Unconditional security of a three state quantum key distribution protocol. , 2004, Physical review letters.

[63]  Richard J. Hughes,et al.  FREE-SPACE QUANTUM-KEY DISTRIBUTION , 1998, quant-ph/9801006.

[64]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[65]  John Preskill,et al.  Secure quantum key distribution with an uncharacterized source. , 2003, Physical review letters.