The Supposition for the Kochen and Specker Theorem Using Sum rule and Product rule

  • Koji NagataEmail author
  • Tadao Nakamura


We investigate a hidden-variable theory introduced by Kochen and Specker. The “hidden” results of measurements are either 1 or − 1. We suppose the validity of Sum rule and Product rule. Kochen and Specker suppose the two operations Sum rule and Product rule commute with each other. It is shown that the two operations Sum rule and Product rule do not commute with each other when we want to avoid the Kochen and Specker paradox. Otherwise we encounter the Kochen and Specker paradox. We mention the supposition for Greenberger, Horne, and Zeilinger paradox. It is discussed that only Product rule is necessary for the paradox. We give up the two paradoxes if (1) Sum rule and Product rule do not commute with each other and (2) Product rule is not valid.


Quantum non locality Quantum measurement theory Formalism 



We thank Prof. Do Ngoc Diep, Prof. Shahrokh Heidari, and Prof. Germano Resconi for valuable comments.

Compliance with Ethical Standards

Conflict of interests

On behalf of all authors, the corresponding author states that there is no conflict of interest.


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Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityKohoku-kuJapan

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