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arXiv · 0905.3801

A short impossibility proof of Quantum Bit Commitment

G. Chiribella·G. M. D'Ariano·P. Perinotti·D. M. Schlingemann·R. F. Werner
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Abstract

Bit commitment protocols, whose security is based on the laws of quantum mechanics alone, are generally held to be impossible on the basis of a concealment-bindingness tradeoff. A strengthened and explicit impossibility proof has been given in: G. M. D'Ariano, D. Kretschmann, D. Schlingemann, and R. F. Werner, Phys. Rev. A 76, 032328 (2007), in the Heisenberg picture and in a C*-algebraic framework, considering all conceivable protocols in which both classical and quantum information are exchanged. In the present paper we provide a new impossibility proof in the Schrodinger picture, greatly simplifying the classification of protocols and strategies using the mathematical formulation in terms of quantum combs, with each single-party strategy represented by a conditional comb. We prove that assuming a stronger notion of concealment--worst-case over the classical information histories--allows Alice's cheat to pass also the worst-case Bob's test. The present approach allows us to restate the concealment-bindingness tradeoff in terms of the continuity of dilations of probabilistic quantum combs with respect to the comb-discriminability distance.

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G. Chiribella, G. M. D'Ariano, P. Perinotti, D. M. Schlingemann, R. F. Werner. 2009-05-23. A short impossibility proof of Quantum Bit Commitment. https://doi.org/10.1016/j.physleta.2013.02.045

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