Entanglement quantification in atomic ensembles

Abstract

Entanglement measures quantify nonclassical correlations present in a quantum system, but can be extremely difficult to calculate, even more so, when information on its state is limited. Here, we consider broad families of entanglement criteria that are based on variances of arbitrary operators and analytically derive the lower bounds these criteria provide for two relevant entanglement measures: the best separable approximation (BSA) and the generalized robustness (GR). This yields a practical method for quantifying entanglement in realistic experimental situations, in particular, when only few measurements of simple observables are available. As a concrete application of this method, we quantify bipartite and multipartite entanglement in spin-squeezed Bose-Einstein condensates of $\sim 500$ atoms, by lower bounding the BSA and the GR only from measurements of first and second moments of the collective spin operator.

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• Multipartite entanglement measures: a review
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• Number-phase uncertainty relations and bipartite entanglement detection in spin ensembles
• Detecting Einstein-Podolsky-Rosen steering in non-Gaussian spin states from conditional spin-squeezing parameters
• Entanglement classification and \emph{non-k}-separability certification via Greenberger-Horne-Zeilinger-class fidelity
• Symmetric quantum states: a review of recent progress
• Assisted metrology and preparation of macroscopic superpositions with split spin-squeezed states
• Linear-scale simulations of quench dynamics
• Entanglement of Local Hidden States
• Universal separability criterion for arbitrary density matrices from causal properties of separable and entangled quantum states
• $su(d)$-squeezing and many-body entanglement geometry in finite-dimensional systems
• Uncertainty relations between quantum Fisher information and entanglement monotones
• Error estimation of different schemes to measure spin-squeezing inequalities
• Detecting genuine multipartite entanglement in multi-qubit devices with restricted measurements
• Exact quantification of bipartite entanglement in unresolvable spin ensembles