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AIP conference proceedings

Foreword: Unperformed Experiments Have No Results

Christopher A. Fuchs, Jan-Åke Larsson, Luigi Accardi, Guillaume Adenier, Christopher A. Fuchs, Gregg S. Jaeger, Andrei Yu. Khrennikov, Jan-Åke Larsson, Stig Stenholm

Published Jan 1, 2009• 0 citations

Abstract

This year in Växjö we thought we would try an experiment—it felt high time for a new result. Much of the foundations discussion of previous years has focussed on EPR‐style arguments and the meaning and experimental validity of various Bell inequality violations. Yet, there is another pillar of the quantum foundations puzzle that has hardly received any attention in our great series of meetings: It is the phenomenon first demonstrated by Kochen and Specker, quantum contextuality. Recently there has been a rapid growth of activity aimed toward better understanding this aspect of quantum mechanics, which Asher Peres sloganized by the phrase, “unperformed experiments have no results.” Below is a sampling of some important papers on the topic for the reader not yet familiar with the subject. What is the source of this phenomenon? Does it depend only on high level features of quantum mechanics, or is it deep in the conceptual framework on which the theory rests? Might it, for instance, arise from the way quantum mechanics amends the classic laws of probability? What are the mathematically simplest ways contextuality can be demonstrated? How might the known results be made amenable to experimental tests? These were the sorts of discussions we hoped the session would foster.

DOI: 10.1063/1.3111451

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This year in Växjö we thought we would try an experiment—it felt high time for a new result. Much of the foundations discussion of previous years has focussed on EPR‐style arguments and the meaning and experimental validity of various Bell inequality violations. Yet, there is another pillar of the quantum foundations puzzle that has hardly received any attention in our great series of meetings: It is the phenomenon first demonstrated by Kochen and Specker, quantum contextuality. Recently there has been a rapid growth of activity aimed toward better understanding this aspect of quantum mechanics, which Asher Peres sloganized by the phrase, “unperformed experiments have no results.” Below is a sampling of some important papers on the topic for the reader not yet familiar with the subject. What is the source of this phenomenon? Does it depend only on high level features of quantum mechanics, or is it deep in the conceptual framework on which the theory rests? Might it, for instance, arise from the way quantum mechanics amends the classic laws of probability? What are the mathematically simplest ways contextuality can be demonstrated? How might the known results be made amenable to experimental tests? These were the sorts of discussions we hoped the session would foster.

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.

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.

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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

It is well known that in quantum mechanics we cannot always define consistently properties that are context independent. Many approaches exist to describe contextual properties, such as Contextuality by Default (CbD), sheaf theory, topos theory, and non-standard or signed probabilities. In this paper, we propose a treatment of contextual properties that is specific to quantum mechanics, as it relies on the relationship between contextuality and indistinguishability. In particular, we propose that if we assume the ontological thesis that quantum particles or properties can be indistinguishable yet different, no contradiction arising from a Kochen–Specker-type argument appears: when we repeat an experiment, we are in reality performing an experiment measuring a property that is indistinguishable from the first, but not the same. We will discuss how the consequences of this move may help us understand quantum contextuality.