New Spin Squeezing and Other Entanglement Tests for Two Mode Systems of Identical Bosons

TL;DR

This paper develops and validates new spin squeezing and entanglement tests tailored for two-mode systems of identical massive bosons, considering symmetrisation and super-selection rules.

Contribution

It introduces novel entanglement criteria that incorporate symmetrisation and super-selection rules, extending previous methods for systems of identical bosons.

Findings

New spin squeezing criteria for bosonic systems.

Validation of existing entanglement tests under new constraints.

Derivation of additional entanglement detection methods.

Abstract

For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrisation principle (SP) and for massive particles also conform to super-selection rules (SSR) that prohibit coherences between differing total particle numbers. Here we consider bi-partitite states for systems of massive bosons, where both the system and subsystems are modes (or sets of modes), particles being associated with differing mode occupancies. To define non-entangled or separable states the subsystem density operators are also required to satisfy the SP and conform to SSR, in contrast to some other approaches. Whilst in the presence of these additional constraints some of the known entanglement criteria are still valid, we present a detailed treatment to establish the validity of known criteria and derive new ones.