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.

arXiv commentfinal version, to appear in PRA

References in corpus (29)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Mixed State Entanglement and Quantum Error Correction
• Three qubits can be entangled in two inequivalent ways
• Concentrating Partial Entanglement by Local Operations
• Distributed Entanglement
• Quantifying Entanglement
• On the volume of the set of mixed entangled states
• Mixed-state entanglement and distillation: is there a ``bound'' entanglement in nature?
• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Entanglement monotones
• Four qubits can be entangled in nine different ways
• Generalized Schmidt decomposition and classification of three-quantum-bit states
• Exact and Asymptotic Measures of Multipartite Pure State Entanglement
• Maximal entanglement versus entropy for mixed quantum states
• Maximizing the entanglement of two mixed qubits
• Maximally entangled mixed states of two qubits
• Estimating entanglement measures in experiments
• Multipartite generalisation of the Schmidt decomposition
• Counterexample to an additivity conjecture for output purity of quantum channels
• The geometric measure of entanglement for symmetric states
• Irreversibility in asymptotic manipulations of entanglement
• Bounds on relative entropy of entanglement for multi-party systems
• An entanglement monotone derived from Grover's algorithm
• Are all maximally entangled states pure?
• 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 (35)

• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Geometric measure of entanglement for pure multipartite states
• Additivity and non-additivity of multipartite entanglement measures
• The geometric measure of multipartite entanglement and the singular values of a hypermatrix
• Entanglement and Discord of superposition of Greenberger-Horne-Zeilinger states
• Classification of Entanglement in Symmetric States
• Entanglement and coherence in Bernstein-Vazirani algorithm
• Matrix permanent and quantum entanglement of permutation invariant states
• How entangled can a multi-party system possibly be?
• Duality and the geometric measure of entanglement of general multiqubit W states
• Entanglement quantification made easy: Polynomial measures invariant under convex decomposition
• Decoherence dynamics of geometric measure of quantum discord and measurement-induced nonlocality for noninertial observers at finite temperature
• A genuine maximally seven-qubit entangled state
• Approximation algorithms for QMA-complete problems
• Multipartite Bell-type Inequality by Generalizing Wigner's Argument
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Theoretical and computational aspects of entanglement
• Tensor rank and entanglement of pure quantum states
• Distillation of genuine tripartite Einstein-Podolsky-Rosen steering
• Symmetric Multiqudit States: Stars, Entanglement, Rotosensors
• Persistence of entanglement in thermal states of spin systems
• Geometric Entanglement of Symmetric States and the Majorana Representation
• Evaluation of two different entanglement measures on a bound entangled state
• Spin Squeezing by means of Driven Superradiance
• Simple permutation-based measure of quantum correlations and maximally-3-tangled states
• Geometric measure of entanglement of symmetric d-qubits is polynomial-time computable
• Finding maximal quantum resources
• Approximation, Proof Systems, and Correlations in a Quantum World
• Completely mixed state is a critical point for three-qubit entanglement
• Nonstrict inequality for Schmidt coefficients of three-qubit states
• Entanglement bound for multipartite pure states based on local measurements
• Effect of Phase Factor in the Geometric Entanglement Measure of Three-Qubit States
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems