Quantum contextuality

Quantum contextuality is a foundational concept in quantum theory. Quantum Contextuality means that in any theory that attempts to explain quantum mechanics deterministically, the measurement result of a quantum observable depends on the specific experimental setup being used to measure that observable, in particular the commuting observables being measured with it.


Kochen and Specker

Later, Simon B. Kochen and Ernst Specker, and separately John Bell, constructed proofs that quantum mechanics is contextual for systems of dimension 3 and greater. In addition, Kochen and Specker constructed an explicitly noncontextual hidden variable model for the two-dimensional qubit case in their paper on the subject.,[1] thereby completing the characterisation of the dimensionality of quantum systems that can demonstrate contextual behaviour. Bell's proof invoked a weaker version of Gleason's theorem, reinterpreting the result to show that quantum contextuality exists only in dimensions greater than two.[2]

Graph theory and optimization

Adán Cabello, Simone Severini, and Andreas Winter introduced a general graph-theoretic framework for studying contextuality of different physical theories. This allowed to show that quantum contextuality is closely related to the Lovász number, an important parameter used in optimization and information theory.[3] By making use of similar techniques, Mark Howard, Joel Wallman, Victor Veitch, and Joseph Emerson have then shown that the Lovász number has a key role in determining the power of quantum computing.[4]

Leibniz's principle

The notion of quantum contextuality due to Spekkens[5] removes the assumption of determinism of outcomes that is present in other forms of contextuality. This breaks the interpretation of contextuality as a direct extension of Nonlocality, and does not treat irreducible randomness as nonclassical. However, such forms of contextuality can be motivated using Leibniz's law of the Identity of indiscernibles; the law applied to physical systems mirrors the modified definition of noncontextuality. This was further explored by Simmons et al,[6] who demonstrated that other notions of contextuality could also be motivated by Leibnizian principles, and could be thought of as tools enabling ontological conclusions from operational statistics.

See also

Notes

  1. ↑ S. Kochen and E.P. Specker, "The problem of hidden variables in quantum mechanics", Journal of Mathematics and Mechanics 17, 59–87 (1967)
  2. ↑ Gleason, A. M, "Measures on the closed subspaces of a Hilbert space", Journal of Mathematics and Mechanics 6, 885–893 (1957).
  3. ↑ A. Cabello, S. Severini, A. Winter, Graph-Theoretic Approach to Quantum Correlations", Physical Review Letters 112 (2014) 040401.
  4. ↑ M. Howard, J. Wallman, V. Veitch, J. Emerson, (19 June 2014), "Contextuality supplies the 'magic' for quantum computation", Nature 510: 351.
  5. ↑ R. Spekkens, "Contextuality for preparations, transformations, and unsharp measurements",Phys. Rev. A 71, 052108 (2005).
  6. ↑ A.W. Simmons, Joel J. Wallman, H. Pashayan, S.D. Bartlett, T. Rudolph, "Contextuality under weak assumptions", New J. Phys. 19 033030, (2017).
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.