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Although it is impossible for a bit commitment protocol to be botharbitrarily concealing and arbitrarily binding, it is possible for it to beboth partially concealing and partially binding. This means that Bob cannot,prior to the beginning of the unveiling phase, find out everything about thebit committed, and Alice cannot, through actions taken after the end of thecommitment phase, unveil whatever bit she desires. We determine upper bounds onthe degrees of concealment and bindingness that can be achieved simultaneouslyin any bit commitment protocol, although it is unknown whether these can besaturated. We do, however, determine the maxima of these quantities in arestricted class of bit commitment protocols, namely those wherein all thesystems that play a role in the commitment phase are supplied by Alice. We showthat these maxima can be achieved using a protocol that requires Alice toprepare a pair of systems in an entangled state, submit one of the pair to Bobat the commitment phase, and the other at the unveiling phase. Finally, wedetermine the form of the trade-off that exists between the degree ofconcealment and the degree of bindingness given various assumptions about thepurity and dimensionality of the states used in the protocol.Comment: 10 pages, 1 figure. Typos correcte

Degrees of concealment and bindingness in quantum bit commitment protocols