Phase diagram for the one-way quantum deficit of two-qubit X states

Abstract

The one-way quantum deficit, a measure of quantum correlation, can exhibit for X quantum states the regions (subdomains) with the phases $\Delta_0$ and $\Delta_{\pi/2}$ which are characterized by constant (i.e., universal) optimal measurement angles, correspondingly, zero and $\pi/2$ with respect to the $z$-axis and a third phase $\Delta_\vartheta$ with the variable (state-dependent) optimal measurement angle $\vartheta$. We build the complete phase diagram of one-way quantum deficit for the XXZ subclass of symmetric X states. In contrast to the quantum discord where the region for the phase with variable optimal measurement angle is very tiny (more exactly, it is a very thin layer), the similar region $\Delta_\vartheta$ is large and achieves the sizes comparable to those of regions $\Delta_0$ and $\Delta_{\pi/2}$. This instils hope to detect the mysterious fraction of quantum correlation with the variable optimal measurement angle experimentally.