When quantum channel preserves product states

TL;DR

This paper characterizes quantum channels that preserve product states, identifying their exact forms and showing they are either local channels, compositions with flip operations, or fix one local state, applicable to finite and infinite dimensions.

Contribution

It provides a complete characterization of channels preserving product states, including their explicit forms and conditions, extending to both finite and infinite-dimensional systems.

Findings

Quantum channels preserving product states are either local, composed with flip operations, or fix a local state.

The characterization applies to both finite- and infinite-dimensional systems.

Explicit forms of such channels are derived.

Abstract

Product states are always considered as the states that don't contain quantum correlation. We discuss here when a quantum channel sends the product states to themselves. The exact forms of such channels are proposed. It is shown that such a quantum channel is a local quantum channel, a composition of a local quantum channel and a flip operation, or such that one of the local states is fixed. Both finite- and infinite-dimensional systems are considered.