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Kochen-Specker Sets with a Mixture of 16 Rank-1 and 14 Rank-2 Projectors for a Three-Qubit System |
S. P. Toh** |
Faculty of Engineering, The University of Nottingham Malaysia Campus, Jalan Broga, 43500 Semenyih, Selangor Darul Ehsan, Malaysia
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Cite this article: |
S. P. Toh 2013 Chin. Phys. Lett. 30 100302 |
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Abstract Kochen-Specker (KS) theorem denies the possibility for the noncontextual hidden variable theories to reproduce the predictions of quantum mechanics. A set of projection operators (projectors) and bases used to show the impossibility of noncontextual definite values assignment is named as the KS set. Since one KS set with a mixture of 16 rank-1 projectors and 14 rank-2 projectors was proposed in 1995 [Kernaghan M and Peres A Phys. Lett. A 198 (1995) 1] for a three-qubit system, there have been plenty of the same type KS sets and we propose a systematic way to produce them. We also propose a probabilistic state-dependent proof of the KS theorem that mainly focuses on the values assignment for all the rank-2 projectors.
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Received: 17 June 2013
Published: 21 November 2013
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PACS: |
03.65.Aa
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(Quantum systems with finite Hilbert space)
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03.65.Ta
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(Foundations of quantum mechanics; measurement theory)
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42.50.Dv
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(Quantum state engineering and measurements)
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[1] Peres A 1993 Quantum Theory: Concepts and Methods (Kluwer, Dordrecht) p196 [2] Kochen S and Specker E P 1967 J. Math. Mech. 17 59 [3] Peres A 1991 J. Phys. A: Math. Gen. 24 L175 [4] Conway J H and Kochen S, reported by Peres A 1993 in Quantum Theory: Concepts and Method (Kluwer, Dordrecht) p114 [5] Kernaghan M 1994 J. Phys. A: Math. Gen. 27 L829 [6] Cabello A, Estebaranz J M and García-Alcaine G 1996 Phys. Lett. A 212 183 [7] Maegell M, Aravind P K, Megill N D and Pavi?i? M 2011 Found. Phys. 41 883 [8] Cabello A and García-Alcaine G 2005 Phys. Lett. A 339 425 [9] Kernaghan M and Peres A 1995 Phys. Lett. A 198 1 [10] Waegell M and Aravind P K 2012 J. Phys. A: Math. Theor. 45 405301 [11] Planat M 2012 Eur. Phys. J. Plus 127 86 [12] Michler M, Weinfurter H and Zukowski M 2000 Phys. Rev. Lett. 84 5457 [13] Huang Y F, Li C F, Zhang Y S, Pan J W and Guo G C 2003 Phys. Rev. Lett. 90 250401 [14] Yang T, Zhang Q, Yin J, Zhao Z, Zukowski M, Chen Z B and Pan J W 2005 Phys. Rev. Lett. 95 240406 [15] Amselem E, Radmark M, Bourennane M and Cabello A 2009 Phys. Rev. Lett. 103 160405 [16] Hasegawa Y, Loidl R, Badurek G, Baron M and Rauch H 2006 Phys. Rev. Lett. 97 230401 [17] Bartosik H, Klepp J, Schmitzer C, Sponar S, Cabello A, Rauch H and Hassegawa Y 2009 Phys. Rev. Lett. 103 040403 [18] Kirchmair G, Z?hringer F, Gerritsma R, Kleinmann M, Gühne O, Cabello A, Blatt R and Roos C F 2009 Nature 460 494 [19] Wei L F, Maruyama K, Wang X B, You J Q and Nori F 2010 Phys. Rev. B 81 174513 [20] Liu B H, Huang Y F, Gong Y X, Sun F W, Zhang Y S, Li C F and Guo G C 2009 Phys. Rev. A 80 044101 [21] Simon C, ?ukowski M, Weinfurter H and Zeilinger A 2000 Phys. Rev. Lett. 85 1783 [22] Yu S and Oh C H 2012 Phys. Rev. Lett. 108 030402 |
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