Degrees of concealment and bindingness in quantum bit commitment protocols

R. W. Spekkens and T. Rudolph
Phys. Rev. A 65, 012310 – Published 11 December 2001
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Abstract

Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partiallyconcealing and partiallybinding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Alice cannot, through actions taken after the end of the commitment phase, unveil whatever bit she desires. We determine upper bounds on the degrees of concealment and bindingness that can be achieved simultaneously in anybit commitment protocol, although it is unknown whether these can be saturated. We do, however, determine the maxima of these quantities in a restricted class of bit commitment protocols, namely, those wherein all the systems that play a role in the commitment phase are supplied by Alice. We show that these maxima can be achieved using a protocol that requires Alice to prepare a pair of systems in an entangled state, submit one of the pair to Bob at the commitment phase, and the other at the unveiling phase. Finally, we determine the form of the trade off that exists between the degree of concealment and the degree of bindingness given various assumptions about the purity and dimensionality of the states used in the protocol.

  • Received 20 June 2001

DOI:https://doi.org/10.1103/PhysRevA.65.012310

©2001 American Physical Society

Authors & Affiliations

R. W. Spekkens1 and T. Rudolph2

  • 1Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7
  • 2Institut für Experimentalphysik, Universität Wien, Boltzmanngasse 5, 1090 Vienna, Austria

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Vol. 65, Iss. 1 — January 2002

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