Equivalence of classicality and separability based on P phase-space representation of symmetric multiqubit states

TL;DR

This paper proves that in symmetric multiqubit systems, the negativity of the P phase-space representation is equivalent to entanglement, linking a classicality measure directly to quantum entanglement.

Contribution

It establishes the equivalence between classicality (via P phase-space negativity) and quantum entanglement in symmetric multiqubit states, a novel theoretical result.

Findings

Negativity of P phase-space representation implies entanglement.

Entanglement implies negativity of P phase-space representation.

The two notions are equivalent in symmetric multiqubit states.

Abstract

Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features -- for which no classical explanation exist -- and their interrelations is of foundational interest. Moreover, recognizing non-classical features carries practical significance in information processing tasks as it offers insights as to why quantum protocols work better than their classical counterparts. We focus here on two celebrated notions of non-classicality viz., negativity of P phase-space representation and entanglement in symmetric multiqubit systems. We prove that they imply each other.