Quantum contextuality

Quantum contextuality is a foundational concept in quantum theory. Quantum Contextuality means that the measurement result of a quantum observable depends on the physical arrangement of a second commuting observable being measured with it (previous or simultaneous) . Such measurement results differ when the measurement of quantum observables are prepared with respect to different commuting observables.

Gleason's theorem

Main article: Gleason's theorem

Andrew Gleason proposed a theorem showing for the first time that Quantum Contextuality exists only in dimensions greater than two.[1] This was pointed out already by Niels Bohr in his paper[2] which says that EPR-like paradoxes occur in the quantum systems without the need for an entangled or composite systems.

Kochen and Specker

Later, Simon B. Kochen and Ernst Specker constructed a mathematically rigorous contextual hidden variable model in their paper on the subject.[3]

Graph theory and optimization

Adan 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.[4] 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.[5]


See also

Notes

  1. ↑ Gleason, A. M, "Measures on the closed subspaces of a Hilbert space", Journal of Mathematics and Mechanics 6, 885–893 (1957).
  2. ↑ N. Bohr, "Can Quantum-Mechanical Description of Physical Reality be Considered Complete?", Phys. Rev. 48, 696–702 (1935).
  3. ↑ S. Kochen and E.P. Specker, "The problem of hidden variables in quantum mechanics", Journal of Mathematics and Mechanics 17, 59–87 (1967).
  4. ↑ A. Cabello, S. Severini, A. Winter, Graph-Theoretic Approach to Quantum Correlations", Physical Review Letters 112 (2014) 040401.
  5. ↑ M. Howard, J. Wallman, V. Veitch, J. Emerson, (19 June 2014), "Contextuality supplies the 'magic' for quantum computation", Nature 510: 351.