Min- and Max- Relative Entropies and a New Entanglement Monotone

Details Min- and Max- Relative Entropies and a New Entanglement Monotone Min- and Max- Relative Entropies and a New Entanglement Monotone

2008-03-19

arxiv.org/abs/0803.2770v3

IEEE Transactions on Information Theory, vol. 55, p.2816-2826, June 2009

Physics

Quantum Physics

published version

Scientific paper

Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new entanglement monotone, which we refer to as the max-relative entropy of entanglement, and which is an upper bound to the relative entropy of entanglement. We also generalize the min- and max-relative entropies to obtain smooth min- and max- relative entropies. These act as parent quantities for the smooth Renyi entropies, and allow us to define the analogues of the mutual information, in the Smooth Renyi Entropy framework. Further, the spectral divergence rates of the Information Spectrum approach are shown to be obtained from the smooth min- and max-relative entropies in the asymptotic limit.

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