dorsal/arxiv
View SchemaMultipartite Classical and Quantum Secrecy Monotones
| Authors | N. J. Cerf, S. Massar, S. Schneider |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0202103 |
| URL | https://arxiv.org/abs/quant-ph/0202103 |
| DOI | 10.1103/PhysRevA.66.042309 |
| Journal | Phys. Rev. A 66, 042309 (2002) |
Abstract
In order to study multipartite quantum cryptography, we introduce quantities which vanish on product probability distributions, and which can only decrease if the parties carry out local operations or carry out public classical communication. These ``secrecy monotones'' therefore measure how much secret correlations are shared by the parties. In the bipartite case we show that the mutual information is a secrecy monotone. In the multipartite case we describe two different generalisations of the mutual information, both of which are secrecy monotones. The existence of two distinct secrecy monotones allows us to show that in multipartite quantum cryptography the parties must make irreversible choices about which multipartite correlations they want to obtain. Secrecy monotones can be extended to the quantum domain and are then defined on density matrices. We illustrate this generalisation by considering tri-partite quantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We show that before carrying out measurements on the state, the parties must make an irreversible decision about what probability distribution they want to obtain.
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"abstract": "In order to study multipartite quantum cryptography, we introduce quantities\nwhich vanish on product probability distributions, and which can only decrease\nif the parties carry out local operations or carry out public classical\ncommunication. These ``secrecy monotones\u0027\u0027 therefore measure how much secret\ncorrelations are shared by the parties. In the bipartite case we show that the\nmutual information is a secrecy monotone. In the multipartite case we describe\ntwo different generalisations of the mutual information, both of which are\nsecrecy monotones. The existence of two distinct secrecy monotones allows us to\nshow that in multipartite quantum cryptography the parties must make\nirreversible choices about which multipartite correlations they want to obtain.\nSecrecy monotones can be extended to the quantum domain and are then defined on\ndensity matrices. We illustrate this generalisation by considering tri-partite\nquantum cryptography based on the Greenberger-Horne-Zeilinger (GHZ) state. We\nshow that before carrying out measurements on the state, the parties must make\nan irreversible decision about what probability distribution they want to\nobtain.",
"arxiv_id": "quant-ph/0202103",
"authors": [
"N. J. Cerf",
"S. Massar",
"S. Schneider"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevA.66.042309",
"journal_ref": "Phys. Rev. A 66, 042309 (2002)",
"title": "Multipartite Classical and Quantum Secrecy Monotones",
"url": "https://arxiv.org/abs/quant-ph/0202103"
},
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