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Trace Functions with Applications in Quantum Physics

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Abstract

We consider both known and not previously studied trace functions with applications in quantum physics. By using perspectives we obtain convexity statements for different notions of residual entropy, including the entropy gain of a quantum channel studied by Holevo and others.

We give new proofs of Carlen-Lieb’s concavity/convexity theorems for certain trace functions, by making use of the theory of operator monotone functions. We then apply these methods in a study of new classes of trace functions.

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Acknowledgements

We thank Peter Harremoës for pointing out that the convexity of the residual entropy of a compound system may be easily inferred by considering it as a sum of relative entropies.

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  1. Institute for International Education, Tohoku University, Sendai, Japan

    Frank Hansen

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  1. Frank Hansen
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Correspondence to Frank Hansen.

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Hansen, F. Trace Functions with Applications in Quantum Physics. J Stat Phys 154, 807–818 (2014). https://doi.org/10.1007/s10955-013-0890-x

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  • DOI: https://doi.org/10.1007/s10955-013-0890-x

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