MLC No-go Theorems Reinterpretation and Extension.pdfVIP

a r X i v : q u a n t - p h / 0 7 0 1 1 5 6 v 5 2 1 M a r 2 0 0 8 No-go Theorem of Quantum Bit Commitment: Reinterpretation and Extension Minh-Dung Dang and Patrick Bellot Institut TELECOM - TELECOM ParisTech (Ecole nationale supe?rieure des te?le?communications - ENST), Department of Network and Computer Science, 46 rue Barrault, 75013 Paris, France (Dated: March 21, 2008) 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 imple- menting secure two-party computations musts have access to a trusted third-party which erases information and thus makes dissipation of heat to the environment. 1 I. INTRODUCTION Bit commitment (BC) and oblivious transfer (OT) are two fundamental primitives of Modern Cryptography, used for the construction of secure computations for generic two- party functions1. Let’s recall the definitions: Definition 1 (Bit Commitment). Bit commitment is a two-phase protocol. In t