On the Geometric Measures of Entanglement

TL;DR

This paper explores generalized geometric measures of entanglement based on distances to invariant sets, providing explicit formulas for bipartite states and introducing a new monotone related to W states in three qubits.

Contribution

It extends the geometric measure of entanglement to new invariant sets and derives explicit forms, including a novel monotone for three-qubit W states.

Findings

Explicit formulas for bipartite entanglement measures.

Introduction of a new monotone based on W states.

Discussion of the measure's properties in three-qubit systems.

Abstract

The geometric measure of entanglement, which expresses the minimum distance to product states, has been generalized to distances to sets that remain invariant under the stochastic reducibility relation. For each such set, an associated entanglement monotone can be defined. The explicit analytical forms of these measures are obtained for bipartite entangled states. Moreover, the three qubit case is discussed and argued that the distance to the W states is a new monotone.