Necessary and sufficient conditions for local creation of quantum discord

TL;DR

This paper characterizes the exact conditions under which local quantum channels can or cannot create quantum discord in quantum states, providing precise criteria for different dimensions and channels.

Contribution

It establishes necessary and sufficient conditions for local channels to create quantum discord, refining previous conjectures and results for both qubit and higher-dimensional systems.

Findings

Local channels cannot create QD unless they are completely decohering or isotropic.

A local channel nullifies QD in any state if and only if it is completely decohering.

Results are applicable to quantum information protocols, especially for qubits.

Abstract

We show that a local channel cannot create quantum discord (QD) for zero QD states of size $d\geq3$ if and only if either it is a completely decohering channel or it is a nontrivial isotropic channel. For the qubit case this propertiy is additionally characteristic to the completely decohering channel or the commutativity-preserving unital channel. In particular, the exact forms of the completely decohering channel and the commutativity-preserving unital qubit channel are proposed. Consequently, our results confirm and improve the conjecture proposed by X. Hu et al. for the case of $d\geq3$ and improve the result proposed by A. Streltsov et al. for the qubit case. Furthermore, it is shown that a local channel nullifies QD in any state if and only if it is a completely decohering channel. Based on our results, some protocols of quantum information processing issues associated with QD, especially for the qubit case, would be experimentally accessible.