# Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications

@article{Shirokov2011MonotonicityOT, title={Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications}, author={Maksim E. Shirokov}, journal={arXiv: Quantum Physics}, year={2011} }

A condition for reversibility (sufficiency) of a channel with respect to a given countable family of states with bounded rank is obtained.
This condition shows that a quantum channel preserving the Holevo quantity of at least one (discrete or continuous) ensemble of states with rank $\leq r$ has the r-partially entanglement-breaking complementary channel. Several applications of this result are considered. In particular, it is shown that coincidence of the constrained Holevo capacity and the… Expand

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