On the symmetry of the seminal Horodecki state

TL;DR

This paper investigates the symmetry properties of the Horodecki 2-qutrit state, revealing its classification within symmetric states governed by a commutative subgroup of U(3), and explores equivalent representations through conjugate subgroups.

Contribution

It demonstrates that the Horodecki state belongs to a class of states with symmetry governed by a commutative subgroup of U(3) and identifies equivalent state representations.

Findings

Horodecki state exhibits symmetry under a commutative subgroup of U(3)

Conjugate subgroups generate new classes of symmetric states

Equivalent representations of the Horodecki state are identified

Abstract

It is shown that the seminal Horodecki 2-qutrit state belongs to the class of states displaying symmetry governed by a commutative subgroup of the unitary group U(3). Taking a conjugate subgroup one obtains another classes of symmetric states and one finds equivalent representations of the Horodecki state.