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arXiv:quant-ph/0701156

MLC No-go Theorems: Reinterpretation and Extension

Minh-Dung Dang, Patrick Bellot

Published Jan 22, 2007• 0 citations

Abstract

In this article, we are interested in the physical model of general quantum protocols implementing secure two-party computations in the light of Mayers' and Lo's & Chau's no-go theorems of bit commitment and oblivious transfer. In contrast to the commonly adobted quantum pure two-party model in the literature where classical communication is normally ignored, we propose an alternative interpretation for the purification of classical communication in two-party protocols by introducing a quantum third party for the classical channel. This interpretation leads to a global three-party model, involving Alice's and Bob's machines and the environment coupled to the macroscopic channel, using the decoherence scheme in quantum measurements. This model could give a more general view on the concealing/binding trade-off of quantum bit commitment protocols. Inspired from this three-party interpretation, we extend the no-go theorems for denying some classes of two-party protocols having access to some particular quantum trusted third-parties, known as quantum two-party oracles. The extension implies that a quantum protocol for implementing secure two-party computations musts have access to a trusted third-party which erases information and thus makes dissipation of heat to the environment.

DOI: 10.48550/arxiv.quant-ph/0701156

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Quantum bit commitment has been known to be impossible by the independent proofs of Mayers, and Lo and Chau, under the assumption that the whole quantum states right before the unveiling phase are static to users. We here provide an unconditionally secure non-static quantum bit commitment protocol with a trusted third party, which is not directly involved in any communications between users and can be limited not to get any information of commitment without being detected by users. We also prove that our quantum bit commitment protocol is not secure without the help of the trusted third party. The proof is basically different from the Mayers-Lo-Chau's no-go theorem, because we do not assume the staticity of the finally shared quantum states between users.

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It is well known, due to the no-go theorems, that perfectly secure bit commitment is impossible. For that reason, there exist many proposals for bit commitment protocols that are secure under certain assumptions (such as the existence of a trusted party, computational hardness, or noisy memories). In this paper, we investigate the minimal assumptions required to obtain a secure bit commitment protocol. We show that it is possible to construct a bit commitment scheme with two parties Alice and Bob as long as there is a third party that is willing to broadcast either entangled qubits for the parties or to produce classical strings that are xor-correlated. We also show that the bit commitment scheme proposed is universally composable.

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