dorsal/arxiv
View SchemaSecrecy extraction from no-signalling correlations
| Authors | Valerio Scarani, Nicolas Gisin, Nicolas Brunner, Lluis Masanes, Sergi Pino, Antonio Acin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0606197 |
| URL | https://arxiv.org/abs/quant-ph/0606197 |
| DOI | 10.1103/PhysRevA.74.042339 |
| Journal | Phys. Rev. A 74, 042339 (2006) |
Abstract
Quantum cryptography shows that one can guarantee the secrecy of correlation on the sole basis of the laws of physics, that is without limiting the computational power of the eavesdropper. The usual security proofs suppose that the authorized partners, Alice and Bob, have a perfect knowledge and control of their quantum systems and devices; for instance, they must be sure that the logical bits have been encoded in true qubits, and not in higher-dimensional systems. In this paper, we present an approach that circumvents this strong assumption. We define protocols, both for the case of bits and for generic $d$-dimensional outcomes, in which the security is guaranteed by the very structure of the Alice-Bob correlations, under the no-signalling condition. The idea is that, if the correlations cannot be produced by shared randomness, then Eve has poor knowledge of Alice's and Bob's symbols. The present study assumes, on the one hand that the eavesdropper Eve performs only individual attacks (this is a limitation to be removed in further work), on the other hand that Eve can distribute any correlation compatible with the no-signalling condition (in this sense her power is greater than what quantum physics allows). Under these assumptions, we prove that the protocols defined here allow extracting secrecy from noisy correlations, when these correlations violate a Bell-type inequality by a sufficiently large amount. The region, in which secrecy extraction is possible, extends within the region of correlations achievable by measurements on entangled quantum states.
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"abstract": "Quantum cryptography shows that one can guarantee the secrecy of correlation\non the sole basis of the laws of physics, that is without limiting the\ncomputational power of the eavesdropper. The usual security proofs suppose that\nthe authorized partners, Alice and Bob, have a perfect knowledge and control of\ntheir quantum systems and devices; for instance, they must be sure that the\nlogical bits have been encoded in true qubits, and not in higher-dimensional\nsystems. In this paper, we present an approach that circumvents this strong\nassumption. We define protocols, both for the case of bits and for generic\n$d$-dimensional outcomes, in which the security is guaranteed by the very\nstructure of the Alice-Bob correlations, under the no-signalling condition. The\nidea is that, if the correlations cannot be produced by shared randomness, then\nEve has poor knowledge of Alice\u0027s and Bob\u0027s symbols. The present study assumes,\non the one hand that the eavesdropper Eve performs only individual attacks\n(this is a limitation to be removed in further work), on the other hand that\nEve can distribute any correlation compatible with the no-signalling condition\n(in this sense her power is greater than what quantum physics allows). Under\nthese assumptions, we prove that the protocols defined here allow extracting\nsecrecy from noisy correlations, when these correlations violate a Bell-type\ninequality by a sufficiently large amount. The region, in which secrecy\nextraction is possible, extends within the region of correlations achievable by\nmeasurements on entangled quantum states.",
"arxiv_id": "quant-ph/0606197",
"authors": [
"Valerio Scarani",
"Nicolas Gisin",
"Nicolas Brunner",
"Lluis Masanes",
"Sergi Pino",
"Antonio Acin"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.74.042339",
"journal_ref": "Phys. Rev. A 74, 042339 (2006)",
"title": "Secrecy extraction from no-signalling correlations",
"url": "https://arxiv.org/abs/quant-ph/0606197"
},
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