Security proof of quantum key distribution with detection efficiency mismatch

Authors:
Chi-hang Fred Fung;Kiyoshi Tamaki;Bing Qi;Hoi-Kw&g Lo;Xi&gfeng Ma
Affiliations:
Department of Physics and Center of Computational and Theoretical Physics, University of Hong Kong, Hong Kong, China;NTT Basic Research Laboratories, NTT Corporation, Kanagawa, Japan and CREST, Kawaguchi, Saitama, Japan;Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical & Computer Engineering, University of Toronto, Toronto, Ontario, Canada;Center for Quantum Information and Quantum Control, Department of Physics and Department of Electrical & Computer Engineering, University of Toronto, Toronto, Ontario, Canada;Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada
Venue:
Quantum Information & Computation
Year:
2009

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Abstract

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.