# Measuring quantum discord using the most distinguishable steered states

## TL;DR

This paper introduces a geometric approach to measure quantum discord by identifying the most distinguishable post-measurement states on the steering ellipsoid, providing a tight upper bound that closely relates to quantum discord.

## Contribution

It analytically determines the maximum distinguishability of steered states for certain classes of two-qubit states and links this to quantum discord measurement.

## Key findings

- Most distinguished steered states yield a tight upper bound on quantum discord.
- Analytical maximum distinguishability is obtained for specific classes of states.
- The approach provides a faithful measure of quantum correlations, closely approximating quantum discord.

## Abstract

Any two-qubit state can be represented, geometrically, as an ellipsoid with a certain size and a center located within the Bloch sphere of one of the qubits. Points of this ellipsoid represent the post-measurement states when the other qubit is measured. Based on the most demolition concept in the definition of quantum discord, we study the amount of demolition when the two post-measurement states, represented as two points on the steering ellipsoid, have the most distinguishability. We use trace distance as a measure of distinguishability and obtain the maximum distinguishability for some classes of states, analytically. Using the optimum measurement that gives the most distinguishable steered states, we extract quantum correlation of the state and compare the result with the quantum discord. It is shown that there are some important classes of states for which the most demolition happens exactly at the most distinguished steered points. Correlations gathered from the most distinguished post-measurement states provide a faithful and tight upper bound touching the quantum discord in most of the cases.