On complementary channels and the additivity problem

Details On complementary channels and the additivity problem On complementary channels and the additivity problem

2005-09-14

arxiv.org/abs/quant-ph/0509101v3

Probab. Theory and Appl., v. 51, 133-143, 2005

Physics

Quantum Physics

11 pages; references added, typos corrected

Scientific paper

We explore complementarity between output and environment of a quantum channel (or, more generally, CP map), making an observation that the output purity characteristics for complementary CP maps coincide. Hence, validity of the mutiplicativity/additivity conjecture for a class of CP maps implies its validity for complementary maps. The class of CP maps complementary to entanglement-breaking ones is described and is shown to contain diagonal CP maps as a proper subclass, resulting in new class of CP maps (channels) for which the multiplicativity/additivity holds. Covariant and Gaussian channels are discussed briefly in this context.

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