Reexamination of quantum bit commitment: The possible and the impossible
Abstract
Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. We give a strengthened and explicit proof of this result. We extend its scope to a much larger variety of protocols, which may have an arbitrary number of rounds, in which both classical and quantum information is exchanged, and which may include aborts and resets. Moreover, we do not consider the receiver to be bound to a fixed “honest” strategy, so that “anonymous state protocols,” which were recently suggested as a possible way to beat the known nogo results, are also covered. We show that any concealing protocol allows the sender to find a cheating strategy, which is universal in the sense that it works against any strategy of the receiver. Moreover, if the concealing property holds only approximately, the cheat goes undetected with a high probability, which we explicitly estimate. The proof uses an explicit formalization of general twoparty protocols, which is applicable to more general situations, and an estimate about the continuity of the Stinespring dilation of a general quantum channel. The result also provides a natural characterization of protocols that fall outside the standard setting of unlimited available technology and thus may allow secure bit commitment. We present such a protocol whose security, perhaps surprisingly, relies on decoherence in the receiver’s laboratory.
 Publication:

Physical Review A
 Pub Date:
 September 2007
 DOI:
 10.1103/PhysRevA.76.032328
 arXiv:
 arXiv:quantph/0605224
 Bibcode:
 2007PhRvA..76c2328D
 Keywords:

 03.67.Dd;
 Quantum cryptography;
 Quantum Physics
 EPrint:
 v1: 26 pages, 4 eps figures. v2: 31 pages, 5 eps figures