Parametrization of spin-1 classical states

TL;DR

This paper provides an explicit parametrization of mixed quantum and classical states for a spin-1 system, analyzing their geometric structure and boundary characteristics.

Contribution

It introduces a detailed parametrization of classical and quantum states for spin-1, revealing their geometric boundary as a family of ellipsoids with specific features.

Findings

Boundary consists of a two-parameter family of ellipsoids

Boundary includes straight lines from mixtures of pure classical states

Classical states are equivalent to separable symmetric two-qubit states

Abstract

We give an explicit parametrization of the set of mixed quantum states and of the set of mixed classical states for a spin--1. Classical states are defined as states with a positive Glauber-Sudarshan P-function. They are at the same time the separable symmetric states of two qubits. We explore the geometry of this set, and show that its boundary consists of a two-parameter family of ellipsoids. The boundary does not contain any facets, but includes straight-lines corresponding to mixtures of pure classical states.