# On the possibility to detect quantum correlation regions with the variable optimal measurement angle

## TL;DR

This paper explores the detection of quantum correlation regions with variable optimal measurement angles, proposing specific states and experimental setups to observe these regions, which are difficult to detect in typical quantum states.

## Contribution

It introduces a family of two-qubit X states enabling experimental exploration of all quantum correlation regions, including those with variable optimal measurement angles.

## Key findings

- Theoretical calculations for one-way quantum deficit are provided.
- Design of an experimental setup for generating the relevant states.
- Numerical simulations suggest experimental resolution of intermediate measurement angle regions.

## Abstract

Quantum correlations described by quantum discord and one-way quantum deficit can contain ordinary regions with {\em constant} (i.e., universal) optimal measurement angle $0$ or $\pi/2$ with respect to the $z$-axis and regions with a {\em variable} (state-dependent) angle of the optimal measurement. The latter regions which are absent in the Bell-diagonal states are very tiny for the quantum discord and cannot be observed experimentally due to various imperfections on the preparation and measurement steps of the experiment. On the contrary, for the one-way quantum deficit we succeeded in getting the special two-qubit X states which seem to allow one to reach all regions of quantum correlation exploiting available quantum optical techniques. These states give possibility to deep investigation of quantum correlations and related optimization problems at new region and its boundaries. In the paper, explicit theoretical calculations applicable to one-way deficit are reported, together with the design of the experimental setup for generating such selected family of states; moreover, there are presented numerical simulations showing that the most inaccessible region with the intermediate optimal measurement angle may be resolved experimentally.