Quantum channels that preserve the commutativity

TL;DR

This paper characterizes local quantum channels that preserve classical states by maintaining commutativity, providing criteria and witnesses for such channels, and analyzing their effects on quantum correlation measures.

Contribution

It offers a complete characterization of commutativity-preserving channels and introduces operational criteria and witnesses for identifying them.

Findings

Quantum correlations cannot be created without non-commuting states.

Channels preserving commutativity do not increase distance-based quantum correlation measures.

Quantum discord can increase or decrease under these channels.

Abstract

We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and only if the local quantum channel preserves the commutativity, i.e., the images of any two commuting states also commute. And then we provide an operational necessary and sufficient criterion for a known quantum channel to preserve the commutativity as well as a single observable to witness an arbitrary unknown commutativity-preserving channel. All the distance-based measures for quantum correlations, e.g., the geometric measure, are non-increasing while the quantum discord defined by von Neumann measurements can be increasing or decreasing under local commutativity-preserving channels.