Entanglement of multiparty stabilizer, symmetric, and antisymmetric states

Abstract

We study various distance-like entanglement measures of multipartite states under certain symmetries. Using group averaging techniques we provide conditions under which the relative entropy of entanglement, the geometric measure of entanglement and the logarithmic robustness are equivalent. We consider important classes of multiparty states, and in particular show that these measures are equivalent for all stabilizer states, symmetric basis and antisymmetric basis states. We rigorously prove a conjecture that the closest product state of permutation symmetric states can always be chosen to be permutation symmetric. This allows us to calculate the explicit values of various entanglement measures for symmetric and antisymmetric basis states, observing that antisymmetric states are generally more entangled. We use these results to obtain a variety of interesting ensembles of quantum states for which the optimal LOCC discrimination probability may be explicitly determined and achieved. We also discuss applications to the construction of optimal entanglement witnesses.

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• On the extreme points of sets of absolulely separable and PPT states
• Deterministic Twirling with Low Resources
• Asymmetry activation and its relation to coherence under permutation operation
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• Two-way classical communication remarkably improves local distinguishability