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arXiv · 1004.4782

Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence

Wojciech Roga·Mark Fannes·Karol Zyczkowski
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Abstract

The Holevo quantity provides an upper bound for the mutual information between the sender of a classical message encoded in quantum carriers and the receiver. Applying the strong sub-additivity of entropy we prove that the Holevo quantity associated with an initial state and a given quantum operation represented in its Kraus form is not larger than the exchange entropy. This implies upper bounds for the coherent information and for 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.

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Wojciech Roga, Mark Fannes, Karol Zyczkowski. 2010-04-27. Universal bounds for the Holevo quantity, coherent information \\ and the Jensen-Shannon divergence. https://doi.org/10.1103/physrevlett.105.040505

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