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Monogamy, entanglement and deep hidden variables

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If you have a question about this talk, please contact Berry Groisman.

Despite over 40 years of research on Bell-type inequalities, the question of non-locality and entanglement, new technical results that have general foundational relevance can still be obtained. In this talk I will present a number of new results that deal with the question of how to discern local, quantum and no-signaling correlations.

I will first introduce some technical results that deal with novel quantum inequalities that strengthen the Tsirelson inequalities and non-trivial no-signaling inequalities that discern no-signaling correlations from general correlations. The latter have striking similarity with the well-known CHSH inequality, yet they are crucially different.

Next I will show interesting relationships that exist between inferences on the surface and subsurface level of a hidden variable theory. Here the surface level deals with experimentally accessible probabilities (e.g., via relative frequencies) and the sub-surface level deals with probabilities that are conditioned on a hidden-variable (or the quantum state). The most interesting such a relationship is the following: any deterministic hidden-variable theory that obeys no- signaling and gives non-local correlations must show randomness at the surface, i.e., the surface probabilities cannot be deterministic. This is the case in Bohmian mechanics but this result shows it to be generic.

Lastly, I intend to discuss monogamy and its relevance to foundations of quantum mechanics. It has been known for a while that entanglement is monogamous, i.e., it can not be shared freely. I will extend the discussion to the shareability and monogamy aspects, not just of entanglement, but also of correlations. It turns out that certain non-local quantum correlations cannot be freely shared, i.e. they are monogamous as well. This raises the question of how shareability (monogamy) of non-local correlations and shareability (monogamy) of quantum entanglement are related. I will show that they are related in a non-trivial, subtle way. This allows for a new - and hopefully illuminating- interpretation of the Bell theorem. This discussion will be extended from quantum correlations to monogamy aspects of more general correlations such as no-signaling and partially local correlations.

Throughout the talk I will show how these topics are related, and comment on the foundational impact of the results obtained.

This talk is part of the philosophy series.

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