Detecting the quantum discord of an unknown state by a single observable

TL;DR

This paper introduces a single observable measurement method to detect quantum discord in unknown states using four copies, providing a practical and efficient approach for $2 imes N$ systems and higher dimensions.

Contribution

It proposes a novel observable that witnesses quantum discord with a simple measurement scheme, enabling experimental detection with minimal resources.

Findings

Provides a necessary and sufficient condition for quantum discord in $2 imes N$ systems.

Establishes a necessary condition for higher-dimensional bipartite systems.

Offers a way to estimate a lower bound of quantum discord from the observable's expectation value.

Abstract

We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for nonzero quantum discord in $2\times N$ systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same easy manner as that of the entanglement witness, moreover a quantum circuit is designed to determine the expectation value of our observable with four simultaneous local qubit-measurements.