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International Journal of Theoretical Physics

, Volume 58, Issue 6, pp 1845–1853 | Cite as

No-Cloning Theorem, Kochen-Specker Theorem, and Quantum Measurement Theories

  • Koji NagataEmail author
  • Tadao Nakamura
  • Ahmed Farouk
  • Do Ngoc Diep
Article

Abstract

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

Keywords

Quantum information theory Quantum measurement theory Quantum computer 

Notes

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsKorea Advanced Institute of Science and TechnologyDaejeonKorea
  2. 2.Department of Information and Computer ScienceKeio UniversityYokohamaJapan
  3. 3.Department of Physics and Computer Science, Faculty of ScienceWilfrid Laurier UniversityWaterlooCanada
  4. 4.TIMASThang Long UniversityHanoiVietnam
  5. 5.Institute of Mathematics, VASTHanoiVietnam

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