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Counterexample to an additivity conjecture for output purity of quantum channels

R. F. Werner·A. S. Holevo
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Abstract

A conjecture arising naturally in the investigation of additivity of classical information capacity of quantum channels states that the maximal purity of outputs from a quantum channel, as measured by the p-norm, should be multiplicative with respect to the tensor product of channels. We disprove this conjecture for p>4.79. The same example (with p=infinity) also disproves a conjecture for the multiplicativity of the injective norm of Hilbert space tensor products.

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R. F. Werner, A. S. Holevo. 2002-03-01. Counterexample to an additivity conjecture for output purity of quantum channels. https://doi.org/10.1063/1.1498491

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