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New Method of Obtaining the Kochen-Specker Theorem

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Quantum Computing:An Environment for Intelligent Large Scale Real Application

Part of the book series: Studies in Big Data ((SBD,volume 33))

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Abstract

We derive a new type of no-hidden-variable theorem based on the assumptions proposed by Kochen and Specker. We consider N spin-1/2 systems. The hidden results of measurement are either \(+1\) or \(-1\) (in \(\hbar /2\) unit). We derive some proposition concerning a quantum expected value under an assumption about the existence of the Bloch sphere in N spin-1/2 systems. However, the hidden variables theory violates the proposition with a magnitude that grows exponentially with the number of particles. Therefore, we have to give up either the existence of the Bloch sphere or the hidden variables theory. Also we discuss a two-dimensional no-hidden-variables theorem of the KS type. Especially, we systematically describe our assertion based on more mathematical analysis using raw data in a thoughtful experiment.

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Acknowledgements

We would like to thank Professor Niizeki and Dr. Ren for valuable comments.

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Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Korea

    Koji Nagata

  2. Department of Information and Computer Science, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan

    Tadao Nakamura

  3. Computer Sciences Department, Faculty of Computers and Information, Mansoura University, Mansoura, Egypt

    Ahmed Farouk

Authors
  1. Koji Nagata
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  2. Tadao Nakamura
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  3. Ahmed Farouk
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Correspondence to Koji Nagata .

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Editors and Affiliations

  1. Faculty of Computers and Information, Cairo University , Cairo, Egypt

    Aboul Ella Hassanien

  2. Faculty of Computer and Information Sciences, Mansoura University, Mansoura, Egypt

    Mohamed Elhoseny

  3. Systems Research Institute, Polish Academy of Sciences , Warsaw, Poland

    Janusz Kacprzyk

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Nagata, K., Nakamura, T., Farouk, A. (2018). New Method of Obtaining the Kochen-Specker Theorem. In: Hassanien, A., Elhoseny, M., Kacprzyk, J. (eds) Quantum Computing:An Environment for Intelligent Large Scale Real Application . Studies in Big Data, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-319-63639-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-63639-9_12

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