Proof of Kochen-Specker Theorem: Conversion of Product Rule to Sum Rule
S.P.Toh1,2, Hishamuddin Zainuddin2
1Faculty of Applied Science, Inti International University College, Persiaran Perdana BBN, Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia2Laboratory of Computational Science and Informatics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
Proof of Kochen-Specker Theorem: Conversion of Product Rule to Sum Rule
S.P.Toh1,2, Hishamuddin Zainuddin2
1Faculty of Applied Science, Inti International University College, Persiaran Perdana BBN, Putra Nilai, 71800 Nilai, Negeri Sembilan, Malaysia2Laboratory of Computational Science and Informatics, Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia
摘要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.
Abstract：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.
(Foundations of quantum mechanics; measurement theory)
引用本文:
S.P.Toh;Hishamuddin Zainuddin. Proof of Kochen-Specker Theorem: Conversion of Product Rule to Sum Rule[J]. 中国物理快报, 2009, 26(7): 70305-070305.
S.P.Toh, Hishamuddin Zainuddin. Proof of Kochen-Specker Theorem: Conversion of Product Rule to Sum Rule. Chin. Phys. Lett., 2009, 26(7): 70305-070305.
[1] Held C 2008 Stanford Encyclopedia of Philosophy URLhttp://plato.stanford.edu/archives/win2008/entries/kochen-specker/ [2] Peres A 1996 Found. Phys. 26 807 [3] Mermin N D 1993 Rev. Mod. Phys. 65 803
2009, Vol. 26 
