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

Abstract

We present a two-state practical quantum bit commitment protocol, the security of which is based on the current technological limitations, namely the non-existence of either stable long-term quantum memories, or non-demolition 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, the phase-and the 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 non-demolition measurements and noisy/bounded quantum memories are allowed. Finally, we discuss errors occurring due to a finite detector efficiency, dark counts and imperfect single-photon sources and show to have the same effects as those of standard quantum cryptography.

Can relativistic bit commitment lead to secure quantum oblivious transfer?

“…Nevertheless, when Bob is limited to bounded or noisy quantum storages, secure QOT can be made possible in practice with two approaches. On one hand, with this technological constraint BCCC can be obtained [66][67][68][69][70][71][72][73][74]. This is because Bob can no longer keep system C in Eq.…”

A brief review on quantum bit commitment

“…al, 25 the authors have proposed a nonrelativistic two-state QBC protocol whose security relies on current technological limitations. In fact there are some disadvantages of using relativistic bit commitment protocols that makes it worthwhile to continue to study nonrelativistic protocols.…”

“…25 This paper addresses several issues related to a practical implementation, e.g. modeling of errors due to noise and equipment imperfections, a quantitative analysis of the effects of noise in the system, the optimal cheating strategy or the protocol's security.…”

“…6,32,[35][36][37][38] It was shown that if the memory is not ideal but has a finite noise, there are protocols whose security will not be compromised as long as the time difference between the commitment and the opening phase is bigger than some threshold value, determined by the noisy characteristics of the memory used. 25 Regarding protocols based on relativistic effects, Kent has been working in this topic for several years, proposing several protocols for unconditionally secure bit commitment. 7,18,19,39,40 Nowadays, with the recent experimental demonstrations of unconditionally secure bit commitment, 3, 8 a broad range of opportunities is now open for a lot of applications.…”

Quantum oblivious set-member decision protocol

“…Furthermore, with the rapid development of the technologies of quantum communication and quantum computation, researchers began to consider quantum methods to solve privacy-preserving problems, such as blind quantum computing [1][2][3][4][5], quantum homornorphic encryption [6], quantum private query [7][8][9][10], quantum bit commitment [11][12][13][14], quantum oblivious transfer [15][16][17] and so on.…”