NDLI: Context-Invariant and Local Quasi Hidden Variable (qHV) Modelling Versus Contextual and Nonlocal HV Modelling

Content Provider	Springer Nature Link
Author	Loubenets, Elena R.
Copyright Year	2015
Abstract	For the probabilistic description of 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 exist for each Hilbert space. In this model, a quantum observable X is represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. This, in particular, implies the specific local qHV (LqHV) model for an N-qudit state and allows us to derive the new exact upper bound on the maximal violation of 2 $$\times \cdots \times $$ 2-setting Bell-type inequalities of any type (either on correlation functions or on joint probabilities) under N-partite joint von Neumann measurements on an N-qudit state. For d = 2, this new upper bound coincides with the maximal violation by an N-qubit state of the Mermin–Klyshko inequality. Based on our results, we discuss the conceptual and mathematical advantages of context-invariant and local qHV modelling.
Starting Page	840
Ending Page	850
Page Count	11
File Format	PDF
ISSN	00159018
Journal	Foundations of Physics
Volume Number	45
Issue Number	7
e-ISSN	15729516
Language	English
Publisher	Springer US
Publisher Date	2015-04-21
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	qHV modelling Nonclassicality Contextuality Quantum nonlocality Bell-type inequalities History and Philosophical Foundations of Physics Quantum Physics Classical and Quantum Gravitation, Relativity Theory Statistical Physics, Dynamical Systems and Complexity Mechanics Philosophy of Science
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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