Multiparticle entanglement criteria for nonsymmetric collective variances

TL;DR

This paper develops a new method to detect complex multiparticle entanglement structures using global observables, providing bounds that are independent of system size and applicable to highly non-symmetric states.

Contribution

It introduces a general scheme for verifying multiparticle entanglement from non-permutationally invariant measurements, including bounds related to the spin structure factor and an improved criterion relaxation.

Findings

Derived bounds for multiparticle entanglement verification

Introduced highly non-symmetric entangled states for experimental realization

Provided an improved, scalable entanglement criterion

Abstract

We introduce a general scheme to detect various multiparticle entanglement structures from global non-permutationally invariant observables. In particular, we derive bounds on the variance of non-permutationally invariant and collective operators for the verification of $k$-party entanglement. For a family of observables related to the spin structure factor, we give quantitative bounds on entanglement that are independent of the total number of particles. We introduce highly non-symmetric states with genuine multipartite entanglement that is verifiable with the presented technique and discuss how they can be prepared with trapped ions exploiting the high degree of control in these systems. As a special case, our framework provides an alternative approach to obtain a tight relaxation of the entanglement criterion by S{\o} rensen and M{\o} lmer [Phys. Rev. Lett. 86, 4431 (2001)] that is free from technical assumptions and allows to calculate the bounds with an improved scaling in the detectable depth.