dorsal/arxiv
View SchemaThe quantum bit commitment: a finite open system approach for a complete classification of protocols
| Authors | Giacomo Mauro D'Ariano |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0209149 |
| URL | https://arxiv.org/abs/quant-ph/0209149 |
Abstract
Mayers, Lo and Chau argued that all quantum bit commitment protocols are insecure, because there is no way to prevent an Einstein-Podolsky-Rosen (EPR) cheating attack. However, Yuen presented some protocols which challenged the previous impossibility argument. Up to now, it is still debated whether there exist or not unconditionally secure protocols. In this paper the above controversy is addressed. For such purpose, a complete classification of all possible bit commitment protocols is given, including all possible cheating attacks. Focusing on 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, involving the two quantum operations encoding the bit values and their respective alternate Kraus decompositions. Such bounds are 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"--according to which it is possible to assume as "openly known" both the initial state and the probability distributions for all secret parameters, which can be then "purified". This approach is also motivated by existence of unitary extensions for any open 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": "Mayers, Lo and Chau argued that all quantum bit commitment protocols are\ninsecure, because there is no way to prevent an Einstein-Podolsky-Rosen (EPR)\ncheating attack. However, Yuen presented some protocols which challenged the\nprevious impossibility argument. Up to now, it is still debated whether there\nexist or not unconditionally secure protocols. In this paper the above\ncontroversy is addressed. For such purpose, a complete classification of all\npossible bit commitment protocols is given, including all possible cheating\nattacks. Focusing on the simplest class of protocols (non-aborting and with\ncomplete and perfect verification), it is shown how naturally a\ngame-theoretical situation arises. For these protocols, bounds for the cheating\nprobabilities are derived, involving the two quantum operations encoding the\nbit values and their respective alternate Kraus decompositions. Such bounds are\ndifferent from those given in the impossibility proof. The whole classification\nand analysis has been carried out using a \"finite open system\" approach. The\ndiscrepancy with the impossibility proof is explained on the basis of the\nimplicit adoption of a \"closed system approach\"--equivalent to modeling the\ncommitment as performed by two fixed machines interacting unitarily in a\noverall \"closed system\"--according to which it is possible to assume as \"openly\nknown\" both the initial state and the probability distributions for all secret\nparameters, which can be then \"purified\". This approach is also motivated by\nexistence of unitary extensions for any open system. However, it is shown that\nthe closed system approach for the classification of commitment protocols\nunavoidably leads to infinite dimensions, which then invalidate the continuity\nargument at the basis of the impossibility proof.",
"arxiv_id": "quant-ph/0209149",
"authors": [
"Giacomo Mauro D\u0027Ariano"
],
"categories": [
"quant-ph"
],
"title": "The quantum bit commitment: a finite open system approach for a complete classification of protocols",
"url": "https://arxiv.org/abs/quant-ph/0209149"
},
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