Workshop on: QUANTUM INFORMATION AND FOUNDATIONS OF QUANTUM MECHANICS

Quantum Mechanics: Axiomatics and connections with Computing and Information Theory
Monogamy, entanglement and deep hidden variables

aula DOTTORATO  MARTED' 14 SETTEMBRE ore 11.00 

Micheal P. Seevinck, University of Utrecht 
>PRESENTATION: Micheal P. Seevinck has been guest lecturer
of many graduate courses in Philosophy and History of Physics, Foundations of Quantum
Mechanics, Thermodynamics and Statistical Physics, in many places as Sydney, Nijmegen,
Utrecht. He also has been teaching assistant for undergraduate courses in Quantum
Mechanics, Foundations of Quantum Theory. His main research interests are in foundations
of quantum mechanics and nonlocality, with particular emphasis on the operational approach.


Abstract 


Despite over 40 years of research on Belltype inequalities, the question of nonlocality 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 nosignaling correlations.
** I will first introduce some technical results that deal with novel quantum inequalities that strengthen the Tsirelson inequalities and nontrivial nosignaling inequalities that discern nosignaling correlations from general correlations. The latter have striking similarity with the wellknown 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 subsurface level deals with probabilities that are conditioned on a hiddenvariable (or the quantum state). The most interesting such a relationship is the following: any deterministic hiddenvariable theory that obeys no signaling and gives nonlocal 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 nonlocal quantum correlations cannot be freely shared, i.e. they are monogamous as well. This raises the question of how shareability (monogamy) of nonlocal correlations and shareability (monogamy) of quantum entanglement are related. I will show that they are related in a nontrivial, 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 nosignaling 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.


