TY - GEN
T1 - Secret, public and quantum correlation cost of triples of random variables
AU - Winter, Andreas
PY - 2005
Y1 - 2005
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33749435442&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2005.1523752
DO - 10.1109/ISIT.2005.1523752
M3 - Conference contribution
AN - SCOPUS:33749435442
SN - 0780391519
SN - 9780780391512
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2270
EP - 2274
BT - Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05
T2 - 2005 IEEE International Symposium on Information Theory, ISIT 05
Y2 - 4 September 2005 through 9 September 2005
ER -