Analytic Expressions for Geometric Measure of Three Qubit States

Abstract

A new method is developed to derive an algebraic equations for the geometric measure of entanglement of three qubit pure states. The equations are derived explicitly and solved in cases of most interest. These equations allow oneself to derive the analytic expressions of the geometric entanglement measure in the wide range of the three qubit systems, including the general class of W-states and states which are symmetric under permutation of two qubits. The nearest separable states are not necessarily unique and highly entangled states are surrounded by the one-parametric set of equally distant separable states. A possibility for the physical applications of the various three qubit states to quantum teleportation and superdense coding is suggested from the aspect of the entanglement.

6 pages, no figure, PRA version

References in corpus (1)

• Connecting the generalized robustness and the geometric measure of entanglement

Cited by in corpus (13)

• Entanglement detection
• The geometric measure of entanglement for symmetric states
• GHZ versus W : Quantum Teleportation through Noisy Channels
• Multiqubit symmetric states with high geometric entanglement
• Three-Tangle for Rank-3 Mixed States: mixture of Greenberger-Horne-Zeilinger, W and flipped W states
• Maximally entangled three-qubit states via geometric measure of entanglement
• Reduced State Uniquely Defines Groverian Measure of Original Pure State
• Duality and the geometric measure of entanglement of general multiqubit W states
• Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
• Geometric Measure of Entanglement and Shared Quantum States
• Universal behavior of the geometric entanglement measure of many-qubit W states
• Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States
• Role of Three-Qubit Mixed-States Entanglement in Teleportation Scheme