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  • Author or Editor: D. Petz x
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Abstract  

The Bregman operator divergence is introduced for density matrices by differentiation of the matrix-valued function xx log x. This quantity is compared with the relative operator entropy of Fujii and Kamei. It turns out that the trace is the usual Umegaki’s relative entropy which is the only intersection of the classes of quasi-entropies and Bregman divergences.

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Abstract  

The Pauli channel acting on 2 × 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M n is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings M nM n are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main examples appear on bipartite systems.

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