Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications
Abstract
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 rpartially entanglementbreaking complementary channel. Several applications of this result are considered. In particular, it is shown that coincidence of the constrained Holevo capacity and the quantum mutual information of a quantum channel at least at one full rank state implies that this channel is entanglementbreaking.
 Publication:

arXiv eprints
 Pub Date:
 June 2011
 arXiv:
 arXiv:1106.3297
 Bibcode:
 2011arXiv1106.3297S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 the improved version of this paper is included in arXiv:1203.0262