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An Isaac Newton Institute Workshop

Quantum Information Theory: Present Status and Future Directions

Quantum and secret correlations

26th August 2004

Author: Antonio Acin (ICFO (Barcelona))

Abstract

Quantum and secret correlations are two valuable resources in Quantum Information Theory and Cryptography, respectively. They both have the property of being monogamous: the more two parties share secret or quantum correlations, the less they are coupled to the environment. The analogies between these two resources become more evident if one compares the usual quantum (secret) correlation manipulation scenario: N parties share a quantum state rho_A1…AN (probability distribution P(A1,...,AN)) that is also entangled (correlated) to the environment (Eve). From an operational point of view, one would like to know 1) how many entangled bits (secret bits) are required for the preparation of the state (probability distribution) and 2) how many entangled bits (secret bits) can be extracted, or distilled, from the state (probability distribution). Exploiting these analogies, the following results can be proven: 1) All two-qubit entangled states allow a secure key distribution when Alice, Bob and Eve perform operations at the single-copy level. 2) The preparation of a probability distribution requires entanglement if and only if secret bits are consumed in an alternative preparation using only classical means. This implies that all the entangled states, independently of their distillability properties, can be mapped into probability distributions containing secret correlations. 3) There exists a cryptographic analog of bound entanglement, known as bound information. As it happens for bound entanglement, bound information can be activated: the mixture of non-distillable probability distributions can lead to a distillable one.