# Characterizing nonclassical correlation using affinity

## TL;DR

This paper introduces a new affinity-based geometric discord measure for bipartite quantum systems, resolving issues of previous measures and providing analytical evaluations for various states, enhancing understanding of quantum correlations.

## Contribution

A novel affinity-based geometric discord measure is proposed, addressing local ancilla problems and enabling analytical evaluation for pure and mixed states.

## Key findings

- Affinity-based discord equals geometric entanglement for pure states.
- Derived lower bounds for mixed states.
- Closed-form formula for 2×n mixed states.

## Abstract

Geometric discord, a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. Original version of this measure is suffered by the local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all criteria of a good measure of quantum correlation of the bipartite system and resolves local ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically the proposed quantity for both pure and mixed states. For an arbitrary pure state, it is shown that affinity based geometric discord equal to geometric measure of entanglement. Further, we obtain a lower bound of this measure for m \times n dimensional arbitrary mixed state and a closed formula of proposed version of geometric discord for 2 \times n dimensional mixed state is obtained. Finally, as an illustration, we have studied the nonlocality of Bell diagonal state, isotropic and Werner states.