Invariance of quantum correlations under local channel for a bipartite quantum state

TL;DR

This paper proves that quantum discord and measurement induced non-locality remain unchanged under local quantum channels only if those channels are invertible, highlighting the special case of local unitaries.

Contribution

It establishes a necessary and sufficient condition for the invariance of quantum correlations under local channels, specifically invertibility.

Findings

Quantum discord and MiN are invariant under invertible local channels.

Invariance holds specifically for local unitary channels.

Non-invertible local channels do not preserve these quantum correlations.

Abstract

We show that the quantum discord and the measurement induced non-locality (MiN) in a bipartite quantum state is invariant under the action of a local quantum channel if and only if the channel is invertible. In particular, these quantities are invariant under a local unitary channel.