On approximation of quantum channels

Abstract

We develop an approximation approach to infinite dimensional quantum channels based on detailed investigation of the continuity properties of entropic characteristics of quantum channels and operations (trace-nonincreasing completely positive maps) as functions of a pair ``channel, input state''. The obtained results are then applied to the following problems: continuity of the $\chi$-capacity as function of a channel; strong additivity of the $\chi$-capacity for infinite dimensional channels; the analytical expression for the convex closure of the output entropy of arbitrary quantum channel.

26 pages

References in corpus (3)

• Mixed State Entanglement and Quantum Error Correction
• On the quantification of entanglement in infinite-dimensional quantum systems
• On complementary channels and the additivity problem

Cited by in corpus (9)

• Measures of quantum correlations in infinite-dimensional systems
• Bipartite quantum systems: on the realignment criterion and beyond
• Characterizing the performance of continuous-variable Gaussian quantum gates
• On the entanglement-assisted classical capacity of infinite-dimensional quantum channels
• The Schmidt number and partially entanglement breaking channels in infinite dimensions
• Monotonicity of the Holevo quantity: a necessary condition for equality in terms of a channel and its applications
• The output entropy of quantum channels and operations
• Optimal form of the Kretschmann-Schlingemann-Werner theorem for energy-constrained quantum channels and operations
• A criterion for coincidence of the entanglement-assisted classical capacity and the Holevo capacity of a quantum channel