Contextinvariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space
Abstract
We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and contextinvariant, reproducing all the von Neumann joint probabilities via nonnegative values of realvalued measures and all the quantum product expectations—via the qHV (classicallike) average of the product of the corresponding random variables. In a contextinvariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every Npartite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasiclassical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)].
 Authors:
 Moscow State Institute of Electronics and Mathematics, Moscow 109028 (Russian Federation)
 Publication Date:
 OSTI Identifier:
 22403119
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Mathematical Physics; Journal Volume: 56; Journal Issue: 3; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; HIDDEN VARIABLES; HILBERT SPACE; PROBABILITY; QUANTUM STATES; RANDOMNESS; SIMULATION; STATISTICAL MODELS
Citation Formats
Loubenets, Elena R. Contextinvariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space. United States: N. p., 2015.
Web. doi:10.1063/1.4913864.
Loubenets, Elena R. Contextinvariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space. United States. doi:10.1063/1.4913864.
Loubenets, Elena R. 2015.
"Contextinvariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space". United States.
doi:10.1063/1.4913864.
@article{osti_22403119,
title = {Contextinvariant quasi hidden variable (qHV) modelling of all joint von Neumann measurements for an arbitrary Hilbert space},
author = {Loubenets, Elena R.},
abstractNote = {We prove the existence for each Hilbert space of the two new quasi hidden variable (qHV) models, statistically noncontextual and contextinvariant, reproducing all the von Neumann joint probabilities via nonnegative values of realvalued measures and all the quantum product expectations—via the qHV (classicallike) average of the product of the corresponding random variables. In a contextinvariant model, a quantum observable X can be represented by a variety of random variables satisfying the functional condition required in quantum foundations but each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. The proved existence of this model negates the general opinion that, in terms of random variables, the Hilbert space description of all the joint von Neumann measurements for dimH≥3 can be reproduced only contextually. The existence of a statistically noncontextual qHV model, in particular, implies that every Npartite quantum state admits a local quasi hidden variable model introduced in Loubenets [J. Math. Phys. 53, 022201 (2012)]. The new results of the present paper point also to the generality of the quasiclassical probability model proposed in Loubenets [J. Phys. A: Math. Theor. 45, 185306 (2012)].},
doi = {10.1063/1.4913864},
journal = {Journal of Mathematical Physics},
number = 3,
volume = 56,
place = {United States},
year = 2015,
month = 3
}

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