Characterizations of Strongly Entanglement Breaking channels for infinite-dimensional quantum systems

TL;DR

This paper characterizes strongly entanglement breaking channels in infinite-dimensional quantum systems, providing necessary and sufficient conditions and exploring their null spaces, which advances understanding of quantum entanglement destruction.

Contribution

It introduces new characterizations of SEB channels in infinite-dimensional systems and links their null spaces to specific subspaces of trace-zero operators.

Findings

Necessary and sufficient conditions for SEB channels.

SEB channels' null spaces correspond to closed self-adjoint subspaces.

Extension of entanglement breaking concepts to infinite dimensions.

Abstract

Entanglement breaking (EB) channels, as completely positive and trace-preserving linear operators, sever the entanglement between the input system and other systems. In the realm of infinite-dimensional systems, a related concept known as strongly entanglement breaking (SEB) channels emerges. This paper delves into characterizations of SEB channels, delineating necessary and sufficient conditions for a channel to be classified as SEB, especially with respect to the commutativity of its range. Moreover, we demonstrate that every closed self-adjoint subspace of trace-zero operators, with the trace norm, is the null space of a SEB channel.