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Quantum privacy: introducing mutual independence

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We introduce the concept of mutual independence—correlations shared between distant parties which are independent of the environment. This notion is more general than the standard idea of a secret key—it is a fully quantum and more general form of privacy. The states which possess mutual independence also generalize the so called private states— those that possess private key. We then show that the problem of distributed compression of quantum information can be solved in terms of mutual independence. We suspect that mutual independence is a highly singular quantity, i.e. that it is positive only on a set of measure zero; furthermore, we believe that its presence is seen on the single copy level. This appears to be born out in the classical case.

This talk is part of the CQIF Seminar series.

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