Geometric measure of entanglement for multipartite quantum states

TL;DR

This paper explores the geometric measure of entanglement for various quantum states, providing explicit calculations for bipartite and multipartite pure and mixed states, including special classes like Werner and isotropic states.

Contribution

It extends the geometric measure of entanglement to multipartite states and computes it for specific classes of mixed states, broadening its applicability.

Findings

Explicit formulas for two-qubit mixed states

Calculation for Werner and isotropic states

Application to certain multipartite mixed states

Abstract

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings [A. Shimony, Ann. NY. Acad. Sci. 755, p.675 (1995) and H. Barnum and N. Linden, J. Phys. A: Math. Gen. 34, p.6787 (2001)], is explored for bipartite and multipartite pure and mixed states. It is determined for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states.