IQI Weekly Seminar

We prove the existence for each Hilbert space of a new model, a context-invariant quasi hidden variable (qHV) model, reproducing all the von Neumann joint probabilities via non-negative values of real-valued measures and every quantum product expectation — via the qHV (classical-like) average of the product of the corresponding random variables. In a context-invariant qHV model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual HV model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of a context-invariant model for each Hilbert space negates the general opinion that, in terms of random variables, the Hilbert space description of all joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of  this new model also implies that every multipartite quantum state admits a local qHV (LqHV) model. Applying this new type of probabilistic modelling for the analysis of quantum violations of Bell-type inequalities, we introduce a new upper bound on the maximal violation by an N-qudit  state of Sx....xS-setting Bell-type inequalities of any type, either on correlation functions or on joint probabilities.

Based on:  doi:10.1063/1.4913864; doi:10.1007/s10701-015-9903-8; doi:10.1088/1751-8113/45/18/185306; doi:10.1063/1.3681905