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Kochen-Specker Theorem as a Precondition for Quantum Computing

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Abstract

We study the relation between the Kochen-Specker theorem (the KS theorem) and quantum computing. The KS theorem rules out a realistic theory of the KS type. We consider the realistic theory of the KS type that the results of measurements are either +1 or −1. We discuss an inconsistency between the realistic theory of the KS type and the controllability of quantum computing. We have to give up the controllability if we accept the realistic theory of the KS type. We discuss an inconsistency between the realistic theory of the KS type and the observability of quantum computing. We discuss the inconsistency by using the double-slit experiment as the most basic experiment in quantum mechanics. This experiment can be for an easy detector to a Pauli observable. We cannot accept the realistic theory of the KS type to simulate the double-slit experiment in a significant specific case. The realistic theory of the KS type can not depicture quantum detector. In short, we have to give up both the observability and the controllability if we accept the realistic theory of the KS type. Therefore, the KS theorem is a precondition for quantum computing, i.e., the realistic theory of the KS type should be ruled out.

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Acknowledgments

We thank Professor Weinstein for valuable discussions.

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Authors and Affiliations

  1. Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Korea

    Koji Nagata

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

    Tadao Nakamura

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  1. Koji Nagata
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  2. Tadao Nakamura
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Correspondence to Koji Nagata.

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Nagata, K., Nakamura, T. Kochen-Specker Theorem as a Precondition for Quantum Computing. Int J Theor Phys 55, 5193–5201 (2016). https://doi.org/10.1007/s10773-016-3140-6

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  • DOI: https://doi.org/10.1007/s10773-016-3140-6

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