Absolutely classical spin states

TL;DR

This paper introduces the concept of absolutely classical spin states, analyzing their properties and bounds, and comparing them to absolutely separable quantum states, to understand their stability under unitary transformations.

Contribution

It defines absolutely classical spin states and derives a lower bound for the maximum inscribed ball within the set of classical states.

Findings

Derived a lower bound for the radius of the maximum ball of absolutely classical states.

Compared properties of absolutely classical states with absolutely separable states.

Analyzed the stability of classicality under unitary transformations for spin states.

Abstract

We introduce the concept of "absolutely classical" spin states, in analogy to absolutely separable states of bi-partite quantum systems. Absolutely classical states are states that remain classical under any unitary transformation applied to them. We investigate the maximum ball of absolutely classical states centered on the fully mixed state that can be inscribed into the set of classical states, and derive a lower bound for its radius as function of the total spin quantum number. The result is compared to the case of absolutely separable states.