Geometric measure of entanglement compared to measures based on fidelity

TL;DR

This paper explores the relationship between the geometric measure of entanglement and fidelity-based measures, establishing their equivalence in certain cases and deriving a useful fidelity expression.

Contribution

It connects geometric and fidelity-based entanglement measures, showing their equivalence and providing a new expression for fidelity in quantum states.

Findings

Geometric and revised geometric measures are equal.

Derived a useful expression for fidelity.

Established a connection between different entanglement measures.

Abstract

One of the biggest problems in the theory of quantum information is the quantification of amount of entanglement in an arbitrary multipartite mixed state. Different axiomatic and operational measures were proposed so far. In this work we will establish a connection between geometric measure of entanglement proposed in [Phys. Rev. A 68, 042307 (2003)] and measures based on fidelity. One result will be, that geometric and revised geometric measure of entanglement proposed in [J. Phys. A: Math. Theor. 40, 3507 (2007)] are equal. Further a useful expression for fidelity is derived.