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A classification of hidden-variable properties

Adam Brandenburger1 and Noson Yanofsky2

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Hidden variables are extra components added to try to banish counterintuitive features of quantum mechanics. We start with a quantum-mechanical model and describe various properties that can be asked of a hidden-variable model. We present six such properties and a Venn diagram of how they are related. With two existence theorems and three no-go theorems (EPR, Bell and Kochen–Specker), we show which properties of empirically equivalent hidden-variable models are possible and which are not. Formally, our treatment relies only on classical probability models, and physical phenomena are used only to motivate which models to choose.


PACS

03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.)

02.50.Cw Probability theory

03.65.Ta Foundations of quantum mechanics; measurement theory

MSC

81P15 Quantum measurement theory

81Qxx General mathematical topics and methods in quantum theory

Subjects

Computational physics

Quantum information and quantum mechanics

Dates

Issue 42 (24 October 2008)

Received 8 January 2008, in final form 28 August 2008

Published 26 September 2008



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