Entanglement of multiparty stabilizer, symmetric, and antisymmetric states

TL;DR

This paper investigates entanglement measures of multipartite states with symmetries, proving equivalences among measures for certain classes and calculating explicit values, revealing antisymmetric states are more entangled.

Contribution

It proves the equivalence of key entanglement measures for stabilizer, symmetric, and antisymmetric states, and confirms that the closest product state for permutation symmetric states can be chosen symmetric.

Findings

Entanglement measures are equivalent for stabilizer, symmetric, and antisymmetric states.

Explicit entanglement values are calculated for symmetric and antisymmetric states.

Antisymmetric states are generally more entangled than symmetric 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.