The geometric measure of entanglement for a symmetric pure state with positive amplitudes

Abstract

In this paper for a class of symmetric multiparty pure states we consider a conjecture related to the geometric measure of entanglement: 'for a symmetric pure state, the closest product state in terms of the fidelity can be chosen as a symmetric product state'. We show that this conjecture is true for symmetric pure states whose amplitudes are all non-negative in a computational basis. The more general conjecture is still open.

Similar results have been obtained independently and with different methods by T-C. Wei and S. Severini, see arXiv:0905.0012v1

References in corpus (8)

• Entanglement detection
• Equivalence of critical scaling laws for many-body entanglement in the Lipkin-Meshkov-Glick model
• Unbounded violation of tripartite Bell inequalities
• Ground state of a tightly bound composite dimer immersed in a Fermi Sea
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Entanglement and local information access for graph states
• Survival of entanglement in thermal states
• Thermal robustness of multipartite entanglement of the 1-D spin 1/2 XY model

Cited by in corpus (25)

• Multiqubit symmetric states with high geometric entanglement
• The maximally entangled symmetric state in terms of the geometric measure
• Majorana representation of symmetric multiqubit states
• Geometric measure of entanglement for pure multipartite states
• Additivity and non-additivity of multipartite entanglement measures
• Restricted numerical range: a versatile tool in the theory of quantum information
• The geometric measure of multipartite entanglement and the singular values of a hypermatrix
• Classification of Entanglement in Symmetric States
• Matrix permanent and quantum entanglement of permutation invariant states
• Building separable approximations for quantum states via neural networks
• Exchange symmetry and global entanglement and full separability
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• Minimal Renyi-Ingarden-Urbanik entropy of multipartite quantum states
• The geometric measure of entanglement of pure states with nonnegative amplitudes and the spectral theory of nonnegative tensors
• Norms and Cones in the Theory of Quantum Entanglement
• State transformations within entanglement classes containing permutation-symmetric states
• Maximal Overlap with a Fully Separable State and Translational Invariance in Multipartite Entangled States
• Overlap with the Separable State and Phase Transition in the Dicke Model: Zero and Finite Temperature
• The Quantum Eigenvalue Problem and Z-Eigenvalues of Tensors
• Calculating Entanglement Eigenvalues for Non-Symmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method
• Entanglement bound for multipartite pure states based on local measurements
• Geometric measure of entanglement of multipartite mixed states
• On the geometric measure of entanglement for pure states
• Geometric Measure of Entanglement and Schmidt Decomposition of Multipartite Systems
• Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement