Generalized spin squeezing inequalities for particles number with quantum fluctuations

TL;DR

This paper extends spin squeezing inequalities to account for particle number fluctuations, enabling more accurate entanglement detection in systems with variable particle counts and quantum fluctuations.

Contribution

The authors generalize existing spin squeezing inequalities to include particle number fluctuations, broadening their applicability for entanglement detection.

Findings

Generalized inequalities hold for all separable states with fluctuating particle numbers.

Coordinate-independent form of inequalities is derived.

Example demonstrates advantages over original inequalities.

Abstract

Particle number fluctuations, no matter how small, are present in experimental set-ups. One should rigorously take these fluctuations into account, especially, for entanglement detection. In this context, we generalize the spin squeezing inequalities introduced by T\'oth et al. in Phys. Rev. Lett. 99, 250405 (2007). These new inequalities are fulfilled by all separable states even when the number of particle is not constant, and may present quantum fluctuations. These inequalities are useful for detecting entanglement in many-body systems when the super-selection rule does not apply, or when only a subspace of the total systems Hilbert space is considered. We also define general dichotomic observables for which we obtain a coordinate independent form of the generalized spin squeezing inequalities. We give an example where our generalized coordinate independent spin squeezing inequalities present a clear advantage over the original ones.