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.
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.
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.
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.
Two entangled particles in threedimensional Hilbert space (per particle) are considered in an EPR-type arrangement. On each side the Kochen-Specker observables {J 2 1,J 2 2,J 2 3} and { ¯ J 2 1, ¯ J 2 2,J 2 3} with [J 2 1, ¯ J 2 1] ̸= 0 are measured. The outcomes of measurements of J 2 3 (via J 2 1,J 2 2) and J 2 3 (via ¯ J 2 1, ¯ J 2 2) are compared. Although formally J 2 3 is associated with the same projection operator, quantum contextuality requires that the outcome depends on the complete disposition of the measurement apparatus, in particular whether J 2 1 or ¯ J 2 1 is measured alongside. Besides complementarity, contextuality [1, 2, 3, 4, 5] is another, more subtle nonclassical feature of quantum mechanics. That is, one and the same physical observable may appear different, depending on the context of measurement; i.e., depending on the particular way it was inferred. Stated differently, the outcome of a physical measurement may depend also on other physical measurements which are coperformed. In Bell’s own words [1, section 5], “The result of an
What if Einstein, Podolsky, and Rosen were right that quantum mechanics is incomplete, and there do exist ‘‘elements-of-reality’’ corresponding to all observables whether or not they are compatible? The implications are surprising. Not only must the values of these elements-of-reality depend upon what measurements are actually performed on the system, but also upon measurements performed at spacelike separation from it! The former dependence has been dubbed ‘‘contextualism,’’ and the latter ‘‘nonlocality.’’ It is important for students to understand the necessity of these two features, if only to reinforce the point that a straightforward classical recasting of quantum theory in terms of pre-existing measurement independent elements-of-reality is not feasible. Unfortunately the argument for contextualism, in particular, is daunting due to its reliance on an elaborate geometrical argument. I aim here to minimize the geometry needed to argue for contextualism by using some ideas inspired by the original arguments of Bell and of Kochen and Specker. Using similar methods, I simplify the closely related geometrical argument for nonlocality due to Heywood and Redhead and to Stairs.
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.