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Noise and measurement errors in a practical two-state quantum bit commitment protocol

Loura, R. Loura ; Almeida, A. ; André, P.S ; Pinto, A. N. ; Mateus, P. ; Paunkovic, N.

Physical Review A Vol. 89, Nº 5, pp. 052336-1 - 052336-15, May, 2014.

ISSN (print): 1050-2947
ISSN (online): 1050-2947

Journal Impact Factor: 2,808 (in 2014)

Digital Object Identifier: 10.1103/PhysRevA.89.052336

We present a two-state practical quantum bit commitment protocol, the security of which is based on the
current technological limitations, namely the nonexistence of either stable long-term quantum memories or
nondemolition measurements. For an optical realization of the protocol, we model the errors, which occur
due to the noise and equipment (source, fibers, and detectors) imperfections, accumulated during emission,
transmission, and measurement of photons. The optical part is modeled as a combination of a depolarizing
channel (white noise), unitary evolution (e.g., systematic rotation of the polarization axis of photons), and two
other basis-dependent channels, namely the phase- and bit-flip channels. We analyze quantitatively the effects
of noise using two common information-theoretic measures of probability distribution distinguishability: the
fidelity and the relative entropy. In particular, we discuss the optimal cheating strategy and show that it is always
advantageous for a cheating agent to add some amount of white noise—the particular effect not being present
in standard quantum security protocols. We also analyze the protocol’s security when the use of (im)perfect
nondemolition measurements and noisy or bounded quantum memories is allowed. Finally, we discuss errors
occurring due to a finite detector efficiency, dark counts, and imperfect single-photon sources, and we show that
the effects are the same as those of standard quantum cryptography.