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

TL;DR

This paper revises and refines a compactness criterion for quantum operations in the strong convergence topology, providing detailed proofs, examples, and applications in quantum information theory.

Contribution

It introduces a revised compactness criterion for quantum operations, with detailed proofs, examples, and new criteria for the existence of limit points in strong convergence.

Findings

Revised compactness criterion for quantum operations

New criteria for limit points in strong convergence

Applications in quantum information theory

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.