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The Kochen-Specker Theorem Based on the Kronecker Delta

  • Koji NagataEmail author
  • Santanu Kumar Patro
  • Tadao Nakamura
Article
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Abstract

We propose the Kochen-Specker theorem that relies on the properties of the Kronecker delta. We introduce the following value \(\sum _{l = 1}^{m} r_{l}(\langle \sigma _{z}\rangle )= 0\). The notation rl(〈σz〉) means the lth “hidden” outcome of quantum measurements when we would measure the expected value 〈σz〉 = 0 in a thoughtful experiment. Surprisingly, we cannot define the value as zero when we accept the Kronecker delta. We cannot determine the “hidden” results for the expected value.

Keywords

Quantum information theory Quantum measurement theory Quantum computing 
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Notes

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Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of MathematicsBerhampur University OdishaIndia
  3. 3.Department of Information and Computer ScienceKeio University YokohamaJapan

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