dorsal/arxiv
View SchemaReexamination of Quantum Bit Commitment: the Possible and the Impossible
| Authors | Giacomo Mauro D'Ariano, Dennis Kretschmann, Dirk Schlingemann, Reinhard F. Werner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605224 |
| URL | https://arxiv.org/abs/quant-ph/0605224 |
| DOI | 10.1103/PhysRevA.76.032328 |
| Journal | Phys. Rev. A 76, 032328 (2007) |
Abstract
Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. In this paper 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 no-go 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 two party protocols, which is applicable to more general situations, and a new 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 a new such protocol whose security, perhaps surprisingly, relies on decoherence in the receiver's lab.
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"abstract": "Bit commitment protocols whose security is based on the laws of quantum\nmechanics alone are generally held to be impossible. In this paper we give a\nstrengthened and explicit proof of this result. We extend its scope to a much\nlarger variety of protocols, which may have an arbitrary number of rounds, in\nwhich both classical and quantum information is exchanged, and which may\ninclude aborts and resets. Moreover, we do not consider the receiver to be\nbound to a fixed \"honest\" strategy, so that \"anonymous state protocols\", which\nwere recently suggested as a possible way to beat the known no-go results are\nalso covered. We show that any concealing protocol allows the sender to find a\ncheating strategy, which is universal in the sense that it works against any\nstrategy of the receiver. Moreover, if the concealing property holds only\napproximately, the cheat goes undetected with a high probability, which we\nexplicitly estimate. The proof uses an explicit formalization of general two\nparty protocols, which is applicable to more general situations, and a new\nestimate about the continuity of the Stinespring dilation of a general quantum\nchannel. The result also provides a natural characterization of protocols that\nfall outside the standard setting of unlimited available technology, and thus\nmay allow secure bit commitment. We present a new such protocol whose security,\nperhaps surprisingly, relies on decoherence in the receiver\u0027s lab.",
"arxiv_id": "quant-ph/0605224",
"authors": [
"Giacomo Mauro D\u0027Ariano",
"Dennis Kretschmann",
"Dirk Schlingemann",
"Reinhard F. Werner"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.76.032328",
"journal_ref": "Phys. Rev. A 76, 032328 (2007)",
"title": "Reexamination of Quantum Bit Commitment: the Possible and the Impossible",
"url": "https://arxiv.org/abs/quant-ph/0605224"
},
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