dorsal/arxiv
View SchemaDegrees of concealment and bindingness in quantum bit commitment protocols
| Authors | R. W. Spekkens, T. Rudolph |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0106019 |
| URL | https://arxiv.org/abs/quant-ph/0106019 |
| DOI | 10.1103/PhysRevA.65.012310 |
| Journal | Phys. Rev. A 65, 012310 (2001) |
Abstract
Although it is impossible for a bit commitment protocol to be both arbitrarily concealing and arbitrarily binding, it is possible for it to be both partially concealing and partially binding. This means that Bob cannot, prior to the beginning of the unveiling phase, find out everything about the bit committed, and Alice cannot, through actions taken after the end of the commitment phase, unveil whatever bit she desires. We determine upper bounds on the degrees of concealment and bindingness that can be achieved simultaneously in any bit commitment protocol, although it is unknown whether these can be saturated. We do, however, determine the maxima of these quantities in a restricted class of bit commitment protocols, namely those wherein all the systems that play a role in the commitment phase are supplied by Alice. We show that these maxima can be achieved using a protocol that requires Alice to prepare a pair of systems in an entangled state, submit one of the pair to Bob at the commitment phase, and the other at the unveiling phase. Finally, we determine the form of the trade-off that exists between the degree of concealment and the degree of bindingness given various assumptions about the purity and dimensionality of the states used in the protocol.
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"abstract": "Although it is impossible for a bit commitment protocol to be both\narbitrarily concealing and arbitrarily binding, it is possible for it to be\nboth partially concealing and partially binding. This means that Bob cannot,\nprior to the beginning of the unveiling phase, find out everything about the\nbit committed, and Alice cannot, through actions taken after the end of the\ncommitment phase, unveil whatever bit she desires. We determine upper bounds on\nthe degrees of concealment and bindingness that can be achieved simultaneously\nin any bit commitment protocol, although it is unknown whether these can be\nsaturated. We do, however, determine the maxima of these quantities in a\nrestricted class of bit commitment protocols, namely those wherein all the\nsystems that play a role in the commitment phase are supplied by Alice. We show\nthat these maxima can be achieved using a protocol that requires Alice to\nprepare a pair of systems in an entangled state, submit one of the pair to Bob\nat the commitment phase, and the other at the unveiling phase. Finally, we\ndetermine the form of the trade-off that exists between the degree of\nconcealment and the degree of bindingness given various assumptions about the\npurity and dimensionality of the states used in the protocol.",
"arxiv_id": "quant-ph/0106019",
"authors": [
"R. W. Spekkens",
"T. Rudolph"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.65.012310",
"journal_ref": "Phys. Rev. A 65, 012310 (2001)",
"title": "Degrees of concealment and bindingness in quantum bit commitment protocols",
"url": "https://arxiv.org/abs/quant-ph/0106019"
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