Quantumness of spin-1 states

TL;DR

This paper explores the quantumness of spin-1 states by deriving an analytic measure based on Hilbert-Schmidt distance, providing insights into the geometry of symmetric entangled states and the classical-quantum boundary.

Contribution

It introduces an explicit analytic formula for the quantumness of pure spin-1 states and explores its implications for mixed states and entanglement geometry.

Findings

Analytic expression for pure state quantumness as a function of eigenvalues.

Numerical evidence that pure state formula bounds mixed state quantumness.

Insights into the geometry of symmetric entangled states.

Abstract

We investigate quantumness of spin-1 states, defined as the Hilbert-Schmidt distance to the convex hull of spin coherent states. We derive its analytic expression in the case of pure states as a function of the smallest eigenvalue of the Bloch matrix and give explicitly the closest classical state for an arbitrary pure state. Numerical evidence is provided that the exact formula for pure states provides an upper bound on the quantumness of mixed states. Due to the connection between quantumness and entanglement we obtain new insights into the geometry of symmetric entangled states.