A Classical Analogue of Entanglement

Collins, Daniel; Popescu, Sandu

HPL-BRIMS-2001-17

Keyword(s): entanglement; quantum information; common randomness; shared secret correlations; non-locality

Abstract: We show that quantum entanglement has a very close classical analogue, namely secret classical correlations. The fundamental analogy stems from the behavior of quantum entanglement under local operations and classical communication and the behavior of secret correlations under local operations and public communication. A large number of derived analogues follow. In particular teleportation is analogous to the one-time-pad, the concept of 'pure state' exists in the classical domain, entanglement concentration and dilution are essentially classical secrecy protocols, and single copy entanglement manipulations have such a close classical analog that the majorization results are reproduced in the classical setting. This analogy allows one to import questions from the quantum domain into the classical one, and vice-versa, helping to get a better understanding of both. Also, by identifying classical aspects of quantum entanglement it allows one to identify those aspects of entanglement which are uniquely quantum mechanical.

13 Pages

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