Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities
arXiv:2203.13547 · doi:10.22331/q-2022-12-29-887
Abstract
Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin- atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels , potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of -level quantum systems.
arXiv comment6 + 9 pages, 2 figures. Final version accepted in Quantum Journal
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