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Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule

Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen–Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≥ 3, these constraints contradict individually with t...

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Main Authors: Toh, Sing Poh, Zainuddin, Hishamuddin
Format: Article
Language:English
Published: Institute of Physics 2009
Online Access:http://psasir.upm.edu.my/id/eprint/16369/1/Proof%20of%20Kochen.pdf
http://psasir.upm.edu.my/id/eprint/16369/
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spelling my.upm.eprints.163692016-01-20T02:29:00Z http://psasir.upm.edu.my/id/eprint/16369/ Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule Toh, Sing Poh Zainuddin, Hishamuddin Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen–Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≥ 3, these constraints contradict individually with the assumption of value definiteness. The two rules are not irrelated and Peres [Found. Phys. 26 (1996) 807] has conceived a method of converting the product rule into a sum rule for the case of two qubits. Here we apply this method to a proof provided by Mermin based on the product rule for a three-qubit system involving nine operators. We provide the conversion of this proof to one based on sum rule involving ten operators. Institute of Physics 2009 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16369/1/Proof%20of%20Kochen.pdf Toh, Sing Poh and Zainuddin, Hishamuddin (2009) Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule. Chinese Physics Letters, 26 (7). 070305-1. ISSN 0256-307X 10.1088/0256-307X/26/7/070305
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Valuation functions of observables in quantum mechanics are often expected to obey two constraints called the sum rule and product rule. However, the Kochen–Specker (KS) theorem shows that for a Hilbert space of quantum mechanics of dimension d ≥ 3, these constraints contradict individually with the assumption of value definiteness. The two rules are not irrelated and Peres [Found. Phys. 26 (1996) 807] has conceived a method of converting the product rule into a sum rule for the case of two qubits. Here we apply this method to a proof provided by Mermin based on the product rule for a three-qubit system involving nine operators. We provide the conversion of this proof to one based on sum rule involving ten operators.
format Article
author Toh, Sing Poh
Zainuddin, Hishamuddin
spellingShingle Toh, Sing Poh
Zainuddin, Hishamuddin
Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
author_facet Toh, Sing Poh
Zainuddin, Hishamuddin
author_sort Toh, Sing Poh
title Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
title_short Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
title_full Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
title_fullStr Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
title_full_unstemmed Proof of Kochen¨CSpecker Theorem: conversion of product Rule to sum rule
title_sort proof of kochen¨cspecker theorem: conversion of product rule to sum rule
publisher Institute of Physics
publishDate 2009
url http://psasir.upm.edu.my/id/eprint/16369/1/Proof%20of%20Kochen.pdf
http://psasir.upm.edu.my/id/eprint/16369/
_version_ 1643826193787518976
score 13.244369

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