Maximally entangled three-qubit states via geometric measure of entanglement

Abstract

Bipartite maximally entangled states have the property that the largest Schmidt coefficient reaches its lower bound. However, for multipartite states the standard Schmidt decomposition generally does not exist. We use a generalized Schmidt decomposition and the geometric measure of entanglement to characterize three-qubit pure states and derive a single-parameter family of maximally entangled three-qubit states. The paradigmatic Greenberger-Horne-Zeilinger (GHZ) and W states emerge as extreme members in this family of maximally entangled states. This family of states possess different trends of entanglement behavior: in going from GHZ to W states the geometric measure and the relative entropy of entanglement and the bipartite entanglement all increase monotonically whereas the three-tangle and bi-partition negativity both decrease monotonically.

final version, to appear in PRA

References in corpus (7)

• Estimating entanglement measures in experiments
• The geometric measure of entanglement for symmetric states
• N-Qubit W States are Determined by their Bipartite Marginals
• Analytic Expressions for Geometric Measure of Three Qubit States
• Does three-tangle properly quantify the three-party entanglement for Greenberger-Horne-Zeilinger-type states?
• Reduced State Uniquely Defines Groverian Measure of Original Pure State
• Geometric Measure of Entanglement and Shared Quantum States

Cited by in corpus (11)

• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Duality and the geometric measure of entanglement of general multiqubit W states
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Theoretical and computational aspects of entanglement
• Evaluation of two different entanglement measures on a bound entangled state
• Spin Squeezing by means of Driven Superradiance
• Approximation, Proof Systems, and Correlations in a Quantum World
• Geometric measure of entanglement of symmetric d-qubits is polynomial-time computable
• Completely mixed state is a critical point for three-qubit entanglement
• Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States