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

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 the nonzero quantum discord in 2×N systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of the quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same way as the entanglement witness. Moreover, a quantum circuit is designed to determine the expectation value of our observable with four simultaneous local qubit measurements. © 2011 American Physical Society.