Constraints on Maximal Entanglement Under Groups of Permutations

TL;DR

This paper characterizes entanglement in symmetric physical systems under permutation groups, revealing how group actions define entanglement classes and establishing bounds on maximal entanglement using group-theoretic methods.

Contribution

It introduces a simplified framework for understanding entanglement under permutation symmetries and derives new bounds on maximal entanglement leveraging group normalizers and subgroups.

Findings

Entanglement classes correspond to group orbits under symmetry actions.

Maximal entanglement bounds are derived using group-theoretic properties.

Symmetry groups like cyclic, dihedral, and polyhedral are analyzed for entanglement structure.

Abstract

We provide a simplified characterization of entanglement in physical systems which are symmetric under the action of subgroups of the symmetric group acting on the party labels. Sets of entanglements are inherently equal, lying in the same orbit under the group action, which we demonstrate for cyclic, dihedral, and polyhedral groups. We then introduce new, generalized relationships for the maxima of those entanglement by exploiting the normalizer and normal subgroups of the physical symmetry group.