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Entropy of a correlation matrix and (in)fidelity between several quantum states

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Making use of the strong subadditivity of entropy we prove that the Holevo quantity for an ensemble of k quantum states is not larger than the entropy of a certain correlation matrix. In the case of k=2 states the minimum over the set of admissible correlation matrices is found to be given by a function of the fidelity between both states. This implies an upper bound for the coherent information and the quantum Jensen—Shannon divergence. Restricting our attention to classical information we bound the transmission distance between any two probability distributions by the entropic distance, which is a concave function of the Hellinger distance.

For larger number of k states in an ensemble we find explicit bounds for the exchange entropy, which could be used to characterize distinguishability between them.

This talk is part of the CQIF Seminar series.

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