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Abstract |
John Bell's celebrated inequalities (BI) constrain the « hidden-variable models » that Einstein had first
envisioned to possibly complete the statistical predictions of quantum physics. The violation of BI by
quantum-mechanical predictions imply that the latter are « non-local ». Most experiments have long focused
on violating textbook BI, involving a pair of two-level quantum systems. Yet, more recently, the investigation
of BI in a many-body context has blossomed, motivated both by the fundamental understanding of the
quantum / classical boundary when the complexity of the system increases ; as well as by the certification of
genuine non-classical properties, such as quantum entanglement, in quantum-technology hardwares.
In this talk, we first explain that Bell's local-hidden-variable models are nothing more than classical statistical
physics models (namely, generalizations of Ising models). We use this insight to construct new algorithms,
inspired by so-called inverse statistical problems in data science, that infer previously-unknown BI from
correlation functions as measured in quantum many-body experiments. These new BI are then analized to
gain insight in the manifestations of many-body entanglement, and in the certification of quantum properties.
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