A note on one-way quantum deficit and quantum discord

TL;DR

This paper explores the relationship between one-way quantum deficit and quantum discord in two-qubit systems, revealing conditions for their equivalence, derivations for X states, and their evolution under phase damping channels.

Contribution

It identifies conditions where quantum deficit and discord share optimal measurements, derives deficit from discord for X states, and links quantum deficit to entanglement of formation.

Findings

Quantum deficit and discord share optimal measurements under certain conditions.

One-way quantum deficit can be derived from quantum discord for X states.

Both measures evolve identically under phase damping channels for specific states.

Abstract

One-way quantum deficit and quantum discord are two important measures of quantum correlations. We revisit the relationship between them in two-qubit systems. We investigate the conditions that both one-way quantum deficit and quantum discord have the same optimal measurement ensembles, and demonstrate that one-way quantum deficit can be derived from the quantum discord for a class of X states. Moreover, we give an explicit relation between one-way quantum deficit and entanglement of formation. We show that under phase damping channel both one-way quantum deficit and quantum discord evolve exactly in the same way for four parameters X states. Some examples are presented in details.