Toward an understanding of entanglement for generalized n-qubit W-states

Abstract

We solve stationarity equations of the geometric measure of entanglement for multi-qubit W-type states. In this way we compute analytically the maximal overlap of one-parameter $n$-qubit and two-parameter four-qubit W-type states and their nearest product states. Possible extensions to arbitrary W-type states and geometrical interpretations of these results are discussed in detail.

V1:10 pages, 3 figures V2: 14 pages, one more section is added for the computation of the maximal overlap probability for the two-parametric W-state in 4-qubit system V3: 17 pages, one more 3-dimensional figure is added. Geometric interpretation of the maximal overlap probability is more clearly discussed

References in corpus (9)

• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Bounds on Multipartite Entangled Orthogonal State Discrimination Using Local Operations and Classical Communication
• Estimating entanglement measures in experiments
• Global entanglement and quantum criticality in spin chains
• Characterization of pure quantum states of multiple qubits using the Groverian entanglement measure
• Analytic Expressions for Geometric Measure of Three Qubit States
• Reduced State Uniquely Defines Groverian Measure of Original Pure State
• Mixed-State Entanglement and Quantum Teleportation through Noisy Channels
• Geometric Measure of Entanglement and Shared Quantum States

Cited by in corpus (2)

• Duality and the geometric measure of entanglement of general multiqubit W states
• Universal behavior of the geometric entanglement measure of many-qubit W states