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arXiv:1304.1292

Recent advances in contextuality tests

Jayne E. Thompson, Paweł Kurzyński, Su‐Yong Lee, Akihito Soeda, Dagomir Kaszlikowski

Published Apr 4, 2013• 3 citations
arXivHTMLPDF

Abstract

Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [Rev. Mod. Phys. 38, 447 (1966)] and Kochen-Specker [J. Math. Mech. 17, 59 (1967)] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.

DOI
10.48550/arxiv.1304.1292

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Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [Rev. Mod. Phys. 38, 447 (1966)] and Kochen-Specker [J. Math. Mech. 17, 59 (1967)] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.
Our everyday experiences support the hypothesis that physical systems exist independently of the act of observation. Concordant theories are characterized by the objective realism assumption whereby the act of measurement simply reveals preexisting well-defined elements of reality. In stark contrast quantum mechanics portrays a world in which reality loses its objectivity and is in fact created by observation. Quantum contextuality as first discovered by Bell [1] and Kochen-Specker [2] captures aspects of this philosophical clash between classical and quantum descriptions of the world. Here we briefly summarize some of the more recent advances in the field of quantum contextuality. We approach quantum contextuality through its close relation to Bell type nonlocal scenarios and highlight some of the rapidly developing tests and experimental implementations.
A realization that came gradually in physics is that the ``elements of reality'' of Einstein, Podolsky, and Rosen are provably nonexistent. Specker initiated a line of thinking in 1960, observing that the outcomes of quantum measurements cannot reveal preexisting properties that are independent of which other measurements are performed. This review discusses the diverse current thinking on the problem of contextuality. The possibilities and problems with experimental verifications are discussed, and the violation of Bell inequalities can be viewed as a special case of contextuality.
Quantum mechanics is an extraordinarily successful scientific theory. But more than 100 years after it was first introduced, the interpretation of the theory remains controversial. This Element introduces some of the most puzzling questions at the foundations of quantum mechanics and provides an up-to-date and forward-looking survey of the most prominent ways in which physicists and philosophers of physics have attempted to resolve them. Topics covered include nonlocality, contextuality, the reality of the wavefunction and the measurement problem. The discussion is supplemented with descriptions of some of the most important mathematical results from recent work in quantum foundations, including Bell's theorem, the Kochen-Specker theorem and the PBR theorem.
This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in 'the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell's assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann's "no-go" theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr's view.
A central result in the foundations of quantum mechanics is the Kochen-Specker theorem. In short, it states that quantum mechanics is in conflict with classical models in which the result of a measurement does not depend on which other compatible measurements are jointly performed. Here, compatible measurements are those that can be performed simultaneously or in any order without disturbance. This conflict is generically called quantum contextuality. In this article, we present an introduction to this subject and its current status. We review several proofs of the Kochen-Specker theorem and different notions of contextuality. We explain how to experimentally test some of these notions and discuss connections between contextuality and nonlocality or graph theory. Finally, we review some applications of contextuality in quantum information processing.
Contextuality is a key feature of quantum mechanics, as was first brought to light by Bohr [Albert Einstein: Philosopher-Scientist, Library of Living Philosophers Vol. VII, edited by P. A. Schilpp (Open Court, 1998), pp. 199–241] and later realized more technically by Kochen and Specker [J. Math. Mech. 17, 59 (1967)]. Isham and Butterfield put contextuality at the heart of their topos-based formalism and gave a reformulation of the Kochen–Specker theorem in the language of presheaves in Isham and Butterfield [Int. J. Theor. Phys. 37, 2669 (1998)]. Here, we broaden this perspective considerably (partly drawing on existing, but scattered results) and show that apart from the Kochen–Specker theorem, Wigner’s theorem, Gleason’s theorem, and Bell’s theorem also relate fundamentally to contextuality. We provide reformulations of the theorems using the language of presheaves over contexts and give general versions valid for von Neumann algebras. This shows that a very substantial part of the structure of quantum theory is encoded by contextuality.