Classicality of spin states

TL;DR

This paper generalizes the concept of classicality to spin states in quantum physics, characterizes classical states for low spins, and provides practical tools to identify non-classical states using linear programming.

Contribution

It introduces a formal definition of classical spin states, characterizes them for spin-1/2 and spin-1, and develops non-classicality witnesses and algorithms for higher spins.

Findings

Classical spin states form a convex set fully characterized for spin-1/2 and spin-1.

For bipartite systems, classical states are a subset of separable states.

Linear programming can determine if a state is classical or not.

Abstract

We extend the concept of classicality in quantum optics to spin states. We call a state ``classical'' if its density matrix can be decomposed as a weighted sum of angular momentum coherent states with positive weights. Classical spin states form a convex set C, which we fully characterize for a spin-1/2 and a spin-1. For arbitrary spin, we provide ``non-classicality witnesses''. For bipartite systems, C forms a subset of all separable states. A state of two spins-1/2 belongs to C if and only if it is separable, whereas for a spin-1/2 coupled to a spin-1, there are separable states which do not belong to C. We show that in general the question whether a state is in C can be answered by a linear programming algorithm.