Classicality witness for two-qubit states

TL;DR

This paper introduces a nonlinear witness to identify classical correlations in two-qubit states, providing a practical method for detecting the absence of quantum discord, especially effective for Bell-diagonal states and feasible in NMR experiments.

Contribution

It presents a new nonlinear witness that is both necessary and sufficient for classicality in Bell-diagonal states and can be experimentally implemented in NMR setups.

Findings

The witness accurately detects classical correlations in two-qubit states.

It is both necessary and sufficient for Bell-diagonal states.

The method is experimentally feasible in NMR systems.

Abstract

In the last few years one realized that if the state of a bipartite system can be written as $\sum_{i,j}p_{ij}|a_{i}>< a_{i}|\otimes |b_{j}> < b_{j}|$, where $\{|a_{i}> \}$ and $\{|b_{j}> \}$ form orthonormal basis for the subsystems and $\{p_{ij}\}$ is a probability distribution, then it possesses at most classical correlations. In this article we introduce a nonlinear witness providing a sufficient condition for classicality of correlations (absence of quantum discord) in a broad class of two-qubit systems. Such witness turns out to be necessary and sufficient condition in the case of Bell-diagonal states. We show that the witness introduced here can be readily experimentally implemented in nuclear magnetic resonance setups.