dorsal/arxiv
View SchemaUnifying classical and quantum key distillation
| Authors | Matthias Christandl, Artur Ekert, Michal Horodecki, Pawel Horodecki, Jonathan Oppenheim, Renato Renner |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0608199 |
| URL | https://arxiv.org/abs/quant-ph/0608199 |
| Journal | Proceedings of the 4th Theory of Cryptography Conference, Lecture Notes in Computer Science vol. 4392, pp. 456-478, 2007 |
Abstract
Assume that two distant parties, Alice and Bob, as well as an adversary, Eve, have access to (quantum) systems prepared jointly according to a tripartite state. In addition, Alice and Bob can use local operations and authenticated public classical communication. Their goal is to establish a key which is unknown to Eve. We initiate the study of this scenario as a unification of two standard scenarios: (i) key distillation (agreement) from classical correlations and (ii) key distillation from pure tripartite quantum states. Firstly, we obtain generalisations of fundamental results related to scenarios (i) and (ii), including upper bounds on the key rate. Moreover, based on an embedding of classical distributions into quantum states, we are able to find new connections between protocols and quantities in the standard scenarios (i) and (ii). Secondly, we study specific properties of key distillation protocols. In particular, we show that every protocol that makes use of pre-shared key can be transformed into an equally efficient protocol which needs no pre-shared key. This result is of practical significance as it applies to quantum key distribution (QKD) protocols, but it also implies that the key rate cannot be locked with information on Eve's side. Finally, we exhibit an arbitrarily large separation between the key rate in the standard setting where Eve is equipped with quantum memory and the key rate in a setting where Eve is only given classical memory. This shows that assumptions on the nature of Eve's memory are important in order to determine the correct security threshold in QKD.
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"abstract": "Assume that two distant parties, Alice and Bob, as well as an adversary, Eve,\nhave access to (quantum) systems prepared jointly according to a tripartite\nstate. In addition, Alice and Bob can use local operations and authenticated\npublic classical communication. Their goal is to establish a key which is\nunknown to Eve. We initiate the study of this scenario as a unification of two\nstandard scenarios: (i) key distillation (agreement) from classical\ncorrelations and (ii) key distillation from pure tripartite quantum states.\n Firstly, we obtain generalisations of fundamental results related to\nscenarios (i) and (ii), including upper bounds on the key rate. Moreover, based\non an embedding of classical distributions into quantum states, we are able to\nfind new connections between protocols and quantities in the standard scenarios\n(i) and (ii).\n Secondly, we study specific properties of key distillation protocols. In\nparticular, we show that every protocol that makes use of pre-shared key can be\ntransformed into an equally efficient protocol which needs no pre-shared key.\nThis result is of practical significance as it applies to quantum key\ndistribution (QKD) protocols, but it also implies that the key rate cannot be\nlocked with information on Eve\u0027s side. Finally, we exhibit an arbitrarily large\nseparation between the key rate in the standard setting where Eve is equipped\nwith quantum memory and the key rate in a setting where Eve is only given\nclassical memory. This shows that assumptions on the nature of Eve\u0027s memory are\nimportant in order to determine the correct security threshold in QKD.",
"arxiv_id": "quant-ph/0608199",
"authors": [
"Matthias Christandl",
"Artur Ekert",
"Michal Horodecki",
"Pawel Horodecki",
"Jonathan Oppenheim",
"Renato Renner"
],
"categories": [
"quant-ph"
],
"journal_ref": "Proceedings of the 4th Theory of Cryptography Conference, Lecture\n Notes in Computer Science vol. 4392, pp. 456-478, 2007",
"title": "Unifying classical and quantum key distillation",
"url": "https://arxiv.org/abs/quant-ph/0608199"
},
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