Relative entropy of entanglement for certain multipartite mixed states

Abstract

We prove conjectures on the relative entropy of entanglement (REE) for two families of multipartite qubit states. Thus, analytic expressions of REE for these families of states can be given. The first family of states are composed of mixture of some permutation-invariant multi-qubit states. The results generalized to multi-qudit states are also shown to hold. The second family of states contain Dür's bound entangled states. Along the way, we have discussed the relation of REE to two other measures: robustness of entanglement and geometric measure of entanglement, slightly extending previous results.

Single column, 22 pages, 9 figures, comments welcome

References in corpus (7)

• Quantifying Entanglement with Witness Operators
• Hierarchies of Geometric Entanglement
• Entanglement of multiparty stabilizer, symmetric, and antisymmetric states
• Entanglement and local information access for graph states
• Random bipartite entanglement from W and W-like states
• Connecting the generalized robustness and the geometric measure of entanglement
• Analytical formula connecting entangled state and the closest disentangled state

Cited by in corpus (14)

• Genuinely Multipartite Concurrence of N-qubit X-matrices
• The geometric measure of entanglement for symmetric states
• Multiparticle entanglement under the influence of decoherence
• Quantifying Unknown Quantum Entanglement via a Hybrid Quantum-Classical Machine Learning Framework
• Exchange symmetry and global entanglement and full separability
• Connections of geometric measure of entanglement of pure symmetric states to quantum state estimation
• $q$-analog qudit Dicke states
• Attainability and lower semi-continuity of the relative entropy of entanglement, and variations on the theme
• Dicke states as matrix product states
• Experimental Entanglement Quantification for Unknown Quantum States in a Semi-Device-Independent Manner
• Stochastic behavior of outcome of Schur-Weyl duality measurement
• Quantifying Multipartite Quantum Entanglement in a Semi-Device-Independent Manner
• Dicke subsystems are entangled
• Asymmetry activation and its relation to coherence under permutation operation