Quantum foundations

Quantum foundations is the study of foundational questions related to quantum mechanics and quantum information theory. Some problems studied by researchers of quantum foundations are, for instance, the issue of the correct interpretation of quantum mechanics, the EPR paradox and the related area of quantum nonlocality and contextuality. A seminal result in quantum foundations is the existence of Bell inequalities, and later also the Kochen–Specker theorem that establish a no-go theorem for certain hidden-variable interpretations of quantum theory.

Areas studied in quantum foundations

  • An interpretation of quantum mechanics is a description of how the mathematical structure of quantum mechanics corresponds to our physical reality. An interpretation must for instance say whether the quantum wave function is ontic, i.e. whether it really exists or is merely a mathematical artifact. It must also find a way to cope with the existence of entanglement. Popular interpretations are, for instance, the Copenhagen interpretation, the many-worlds interpretation and the pilot wave theory.
  • Quantum nonlocality studies the counterintuitive result that quantum theory allows correlations between spatially separated systems that are stronger than in any classical theory, or even in any local-realist description of reality. Nonlocality is an instance of quantum contextuality. A situation is contextual when the value of an observable depends on the context in which it is measured. There are ways to measure the amount of contextuality of a system,[1] which leads to the notion of strong contextuality as is demonstrated in, for instance, the GHZ state. Some links between the computational speedup of a quantum computer with respect to a classical computer and the existence of a sufficient amount of contextuality in the computation have also been found.[2]
  • Supposing that the laws of physics were not governed by quantum mechanics, we might still expect some properties of quantum mechanics to continue to hold. To study which properties, physicists can consider foil theories.[3] These are abstract models that might govern the physics of a different universe. For instance, it has been shown that results like the no-cloning theorem or the existence of incompatible measurements holds in any generalised probabilistic theory that is not classical.[4][5] Some well-known foil theories are Spekkens toy model, which is very similar to stabilizer quantum theory, except that it allows a hidden-variable model, the strongly nonlocal Popescu–Rohrlich boxes violate Tsirelson's bound, so that they exhibit even stronger nonlocality than quantum mechanics,[6] and the Euclidean Jordan algebras originally introduced as an algebraic generalisation of the space of observables of quantum theory.
  • The mathematical formulation of quantum mechanics is not very intuitively sensible. As a result, some physicists have taken it upon themselves to find some physical principles from which the laws of quantum mechanics can be derived, similar to how Einstein derived relativity using his equivalence principle. Although a search for such principles dates back to von Neumann and his quantum logic, modern approaches were instigated by Fuchs,[7] which lead to the first modern reconstruction of quantum theory by Hardy.[8] In his wake other reconstructions using different frameworks and axioms were found.[9][10]

Other areas of interest are, for instance, classifying the different types and classes of entanglement, the existence of SIC-POVMs and the study of different types of resource theories.

See also

References

  1. ↑ Abramsky, Samson; Barbosa, Rui Soares; Mansfield, Shane (2017-08-04). "Contextual Fraction as a Measure of Contextuality". Physical Review Letters. 119 (5): 050504. arXiv:1705.07918. Bibcode:2017PhRvL.119e0504A. doi:10.1103/PhysRevLett.119.050504. PMID 28949723.
  2. ↑ Bermejo-Vega, Juan; Delfosse, Nicolas; Browne, Dan E.; Okay, Cihan; Raussendorf, Robert (2017-09-21). "Contextuality as a Resource for Models of Quantum Computation with Qubits". Physical Review Letters. 119 (12): 120505. arXiv:1610.08529. Bibcode:2017PhRvL.119l0505B. doi:10.1103/PhysRevLett.119.120505. PMID 29341645.
  3. ↑ Chiribella, Giulio (2016). Quantum Theory: Informational Foundations and Foils. Springer.
  4. ↑ Barrett, Jonathan (2007-03-05). "Information processing in generalized probabilistic theories". Physical Review A. 75 (3): 032304. arXiv:quant-ph/0508211. Bibcode:2007PhRvA..75c2304B. doi:10.1103/PhysRevA.75.032304.
  5. ↑ Plávala, Martin (2016-10-12). "All measurements in a probabilistic theory are compatible if and only if the state space is a simplex". Physical Review A. 94 (4): 042108. arXiv:1608.05614. Bibcode:2016PhRvA..94d2108P. doi:10.1103/PhysRevA.94.042108.
  6. ↑ Popescu, Sandu; Rohrlich, Daniel (1994-03-01). "Quantum nonlocality as an axiom". Foundations of Physics. 24 (3): 379–385. Bibcode:1994FoPh...24..379P. doi:10.1007/BF02058098.
  7. ↑ Fuchs, Christopher A. (2002-05-08). "Quantum Mechanics as Quantum Information (and only a little more)". arXiv:quant-ph/0205039.
  8. ↑ Hardy, Lucien (2001-01-03). "Quantum Theory From Five Reasonable Axioms". arXiv:quant-ph/0101012.
  9. ↑ Chiribella, Giulio; D’Ariano, Giacomo Mauro; Perinotti, Paolo (2011-07-11). "Informational derivation of quantum theory". Physical Review A. 84 (1): 012311. arXiv:1011.6451. Bibcode:2011PhRvA..84a2311C. doi:10.1103/PhysRevA.84.012311.
  10. ↑ Barnum, Howard; Müller, Markus P.; Ududec, Cozmin (2014). "Higher-order interference and single-system postulates characterizing quantum theory". New Journal of Physics. 16 (12): 123029. arXiv:1403.4147. Bibcode:2014NJPh...16l3029B. doi:10.1088/1367-2630/16/12/123029.
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