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.Comment: 15 pages, revtex
