Secret, public and quantum correlation cost of triples of random variables

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Abstract

The inverse of Maurer's secret key distillation problem from (many independent realisations of) a triple of random variables X, Y, Z by two players (Alice and Bob) against an eavesdropper (Eve) is considered: the formation of the joint distribution (up to local degrading of Z) from secret key and public communication. We determine the asymptotically minimal amount of secret key for this task, and indeed the full trade-off of secret (between Alice and Bob) vs. public (shared between Alice, Bob and Eve) correlation for this problem. Our result generalises a theorem of Wyner on the "common information of a pair of random variables", which is recovered as the special case of Z being independent of XY. We investigate the secret key required as a function of the probability distribution and compare to an analogous notion based on prior shared entanglement.

Original languageEnglish
Title of host publicationProceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05
Pages2270-2274
Number of pages5
DOIs
StatePublished - 2005
Externally publishedYes
Event2005 IEEE International Symposium on Information Theory, ISIT 05 - Adelaide, Australia
Duration: 4 Sep 20059 Sep 2005

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2005
ISSN (Print)2157-8099

Conference

Conference2005 IEEE International Symposium on Information Theory, ISIT 05
Country/TerritoryAustralia
CityAdelaide
Period4/09/059/09/05

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