Tight continuity bounds for the quantum conditional mutual information, for the Holevo quantity and for capacities of quantum channels
Abstract
We start with Fannes' type and Winter's type tight continuity bounds for the quantum conditional mutual information and their specifications for states of special types. Then we analyse continuity of the Holevo quantity with respect to nonequivalent metrics on the set of discrete ensembles of quantum states. We show that the Holevo quantity is continuous on the set of all ensembles of m states with respect to all the metrics if either m or the dimension of underlying Hilbert space is finite and obtain Fannes' type tight continuity bounds for the Holevo quantity in this case. In general case conditions for local continuity of the Holevo quantity for discrete and continuous ensembles are found. Winter's type tight continuity bound for the Holevo quantity under constraint on the average energy of ensembles is obtained and applied to the system of quantum oscillators. The above results are used to obtain tight and closetotight continuity bounds for basic capacities of finitedimensional channels (refining the LeungSmith continuity bounds).
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.09047
 Bibcode:
 2015arXiv151209047S
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory;
 Mathematical Physics
 EPrint:
 39 pages, significantly extended version, in v.2 tight and closetotight continuity bounds for capacities of finitedimensional quantum channels are added, in v.3 the section devoted to the Holevo capacity is revised, in v.4 applications to the multimode quantum oscillator are revised and extended, in v.5,6 minor corrections and modifications are made, in v.7 Proposition 3 is strengthened