TY - JOUR

T1 - A short impossibility proof of quantum bit commitment

AU - Chiribella, G.

AU - D'Ariano, G. M.

AU - Perinotti, P.

AU - Schlingemann, D. M.

AU - Werner, R. F.

N1 - Funding information: G.M.D. acknowledges interesting discussions with H. Yuen, H.K. Lo, and C. Bennett. G.C., G.M.D., P.P. acknowledge A. Bisio for useful observations. G.C. is supported the National Basic Research Program of China (973) 2011CBA00300 ( 2011CBA00301 ), by the National Natural Science Foundation of China through Grants 61033001 and 61061130540 , and by the 1000 Youth Fellowship Program of China . G.C., G.M.D., and P.P. acknowledge support by EC through projects CORNER and COQUIT.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

M3 - Article

VL - 377

SP - 1076

EP - 1087

JO - Phys. Lett. A

JF - Phys. Lett. A

SN - 1873-2410

SN - 1873-2429

ER -