Compactness criterion for families of quantum operations in the strong convergence topology and its applications

Abstract

A revised version of the compactness criterion for families of quantum operations in the strong convergence topology (obtained previously) is presented, along with a more detailed proof and the examples showing the necessity of this revision. Several criteria for the existence of a limit point of a sequence of quantum operations w.r.t. the strong convergence are obtained and discussed. Applications in different areas of quantum information theory are described.

30 pages, any comments and references are welcome

References in corpus (4)

• The structure of degradable quantum channels
• Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
• On the construction of a quantum channel corresponding to non-commutative graph for a qubit interacting with quantum oscillator
• Computable lower bounds on the entanglement cost of quantum channels