Quantum correlation induced by the average distance between the reduced states

TL;DR

This paper introduces a new quantum correlation measure based on the average distance between reduced states, which differs from existing measures like quantum discord and measurement-induced nonlocality, and provides analytical formulas and comparisons.

Contribution

It proposes a novel quantum correlation measure based on average distances, with analytical formulas and comparisons to existing measures like QD and EOF.

Findings

Only product states lack this quantum correlation.

For pure states, it is twice the measurement-induced nonlocality.

It is smaller than quantum discord and entanglement of formation for pure states.

Abstract

A new quantum correlation in terms of the average distance between the reduced state and the $i$-th output reduced states under local von Neumann measurements is proposed. It is shown that only the product states do not contain this quantum correlation and thus it is different from both the quantum discord (QD) [Phys. Rev. Lett. \textbf{88}, 017901 (2001)] and the measurement-induced nonlocality (MIN) [Phys. Rev. Lett. \textbf{106}, 120401(2011)]. For pure states, it is twice of the quantity MIN, and is smaller than QD and entanglement of formation (EOF). A general analytical formula is given and a lower bound for the two qubits case is obtained. Furthermore, we compare it with EOF and QD through the Werner state and the isotropic state respectively.