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For all the joint von Neumann measurements on a D-dimensional quantum system,we present the specific example of a context-invariant quasi hidden variable(qHV) model, proved in [Loubenets, J. Math. Phys. 56, 032201 (2015)] to existfor each Hilbert space. In this model, a quantum observable X is represented bya variety of random variables satisfying the functional condition required inquantum foundations but, in contrast to a contextual model, each of theserandom variables equivalently models X under all joint von Neumannmeasurements, regardless of their contexts. This, in particular, implies thespecific local qHV (LqHV) model for an N-qudit state and allows us to derivethe new exact upper bound on the maximal violation of 2x...x2-setting Bell-typeinequalities of any type (either on correlation functions or on jointprobabilities) under N-partite joint von Neumann measurements on an N-quditstate. For d=2, this new upper bound coincides with the maximal violation by anN-qubit state of the Mermin-Klyshko inequality. Based on our results, wediscuss the conceptual and mathematical advantages of context-invariant andlocal qHV modelling.

Context-invariant and local quasi hidden variable (qHV) modelling versus contextual and nonlocal HV modelling