Entanglement Measures for Intermediate Separability of Quantum States

TL;DR

This paper introduces a family of entanglement measures R_m that detect intermediate levels of separability in multi-qubit states, providing a nuanced tool for characterizing quantum entanglement.

Contribution

The paper proposes a new family of entanglement measures R_m that generalize existing measures and can distinguish different separability structures in quantum states.

Findings

R_m measures vanish for m-separable states.

R_m reduces to known measures for m=2 and m=n.

GHZ and W states show distinct R_m behaviors.

Abstract

We present a family of entanglement measures R_m which act as indicators for separability of n-qubit quantum states into m subsystems for arbitrary 2 \leq m \leq n. The measure R_m vanishes if the state is separable into m subsystems, and for m = n it gives the Meyer-Wallach measure while for m = 2 it reduces, in effect, to the one introduced recently by Love et al. The measures R_m are evaluated explicitly for the GHZ state and the W state (and its modifications, the W_k states) to show that these globally entangled states exhibit rather distinct behaviors under the measures, indicating the utility of the measures R_m for characterizing globally entangled states as well.