Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
Multiparticle entanglement criteria for nonsymmetric collective variances
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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.
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Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.
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Estimating the best separable approximation of non-pure spin-squeezed states
Lower bounds on the best separable approximation distance for non-pure spin-squeezed states are obtained from the complete set of spin-squeezing inequalities, with symmetry-exploiting optimization for upper bounds, revealing finite-temperature entanglement in ordered phases of the XXZ model.
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Entanglement Certification $-$ From Theory to Experiment
Reviews paradigmatic entanglement quantifiers and state-of-the-art detection/certification methods, with emphasis on assumptions about states and measurements.