Circulant quantum channels and its applications

TL;DR

This paper introduces circulant quantum channels, characterizes their structure, and explores their applications, including entanglement-breaking properties and bounds on quantum coherence, offering new insights into quantum information processing.

Contribution

It defines a new subclass of quantum channels, characterizes their properties, and demonstrates their applications in quantum coherence and bipartite systems.

Findings

Circulant quantum channels have images exactly the set of circulant matrices.

These channels are entanglement-breaking, reducing resource costs for quantum correlation erasure.

Applications include tighter bounds on quantum coherence and characterizations in bipartite systems.

Abstract

This note introduces a family of circulant quantum channels -- a subclass of the mixed-permutation channels -- and investigates its key structural and operational properties. We show that the image of the circulant quantum channel is precisely the set of circulant matrices. This characterization facilitates the analysis of arbitrary $n$-th order Bargmann invariants. Furthermore, we prove that the channel is entanglement-breaking, implying a substantially reduced resource cost for erasing quantum correlations compared to a general mixed-permutation channel. Applications of this channel are also discussed, including the derivation of tighter lower bounds for $\ell_p$-norm coherence and a characterization of its action in bipartite systems.