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13 October 2014 Misinterpretation of statistical distance in security of quantum key distribution shown by simulation
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Abstract
This study will test an interpretation in quantum key distribution (QKD) that trace distance between the distributed quantum state and the ideal mixed state is a maximum failure probability of the protocol. Around 2004, this interpretation was proposed and standardized to satisfy both of the key uniformity in the context of universal composability and operational meaning of the failure probability of the key extraction. However, this proposal has not been verified concretely yet for many years while H. P. Yuen and O. Hirota have thrown doubt on this interpretation since 2009. To ascertain this interpretation, a physical random number generator was employed to evaluate key uniformity in QKD. In this way, we calculated statistical distance which correspond to trace distance in quantum theory after a quantum measurement is done, then we compared it with the failure probability whether universal composability was obtained. As a result, the degree of statistical distance of the probability distribution of the physical random numbers and the ideal uniformity was very large. It is also explained why trace distance is not suitable to guarantee the security in QKD from the view point of quantum binary decision theory.
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Takehisa Iwakoshi and Osamu Hirota "Misinterpretation of statistical distance in security of quantum key distribution shown by simulation", Proc. SPIE 9254, Emerging Technologies in Security and Defence II; and Quantum-Physics-based Information Security III, 92540L (13 October 2014); https://doi.org/10.1117/12.2068143
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