dorsal/arxiv
View SchemaThe quantum bit commitment: a complete classification of protocols
| Authors | Giacomo Mauro D'Ariano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209150 |
| URL | https://arxiv.org/abs/quant-ph/0209150 |
Abstract
This paper addresses the controversy between Mayers, Lo and Chau on one side, and Yuen on the opposite side, on whether there exist or not unconditionally secure protocols. For such purpose, a complete classification of all possible bit commitment protocols is given, including all possible cheating attacks. For the simplest class of protocols (non-aborting and with complete and perfect verification), it is shown how naturally a game-theoretical situation arises. For these protocols, bounds for the cheating probabilities are derived, which turn out to be different from those given in the impossibility proof. The whole classification and analysis has been carried out using a "finite open system" approach. The discrepancy with the impossibility proof is explained on the basis of the implicit adoption of a "closed system approach"--equivalent to modeling the commitment as performed by two fixed machines interacting unitarily in a overall "closed system". However, it is shown that the closed system approach for the classification of commitment protocols unavoidably leads to infinite dimensions, which then invalidate the continuity argument at the basis of the impossibility proof.
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"abstract": "This paper addresses the controversy between Mayers, Lo and Chau on one side,\nand Yuen on the opposite side, on whether there exist or not unconditionally\nsecure protocols. For such purpose, a complete classification of all possible\nbit commitment protocols is given, including all possible cheating attacks. For\nthe simplest class of protocols (non-aborting and with complete and perfect\nverification), it is shown how naturally a game-theoretical situation arises.\nFor these protocols, bounds for the cheating probabilities are derived, which\nturn out to be different from those given in the impossibility proof. The whole\nclassification and analysis has been carried out using a \"finite open system\"\napproach. The discrepancy with the impossibility proof is explained on the\nbasis of the implicit adoption of a \"closed system approach\"--equivalent to\nmodeling the commitment as performed by two fixed machines interacting\nunitarily in a overall \"closed system\". However, it is shown that the closed\nsystem approach for the classification of commitment protocols unavoidably\nleads to infinite dimensions, which then invalidate the continuity argument at\nthe basis of the impossibility proof.",
"arxiv_id": "quant-ph/0209150",
"authors": [
"Giacomo Mauro D\u0027Ariano"
],
"categories": [
"quant-ph"
],
"title": "The quantum bit commitment: a complete classification of protocols",
"url": "https://arxiv.org/abs/quant-ph/0209150"
},
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