Characterizing generalized axisymmetric quantum states in $d\times d$ systems

TL;DR

This paper introduces a family of highly symmetric bipartite quantum states in arbitrary dimensions, characterizes their entanglement properties, and solves the separability problem for a subset, revealing bound entanglement and Schmidt numbers.

Contribution

It defines a new class of symmetric quantum states, solves the separability problem for part of this class, and estimates entanglement properties in higher dimensions.

Findings

A subspace of these states is separable.

A sizable part of the family is bound entangled.

Schmidt numbers are characterized for $d=3$.

Abstract

We introduce a family of highly symmetric bipartite quantum states in arbitrary dimensions. It consists of all states that are invariant under local phase rotations and local cyclic permutations of the basis. We solve the separability problem for a subspace of these states and show that a sizable part of the family is bound entangled. We also calculate some of the Schmidt numbers for the family in $d = 3$, thereby characterizing the dimensionality of entanglement. Our results allow us to estimate entanglement properties of arbitrary states, as general states can be symmetrized to the considered family by local operations.