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On Counterfactuals and Contextuality

Karl Svozil

Published Jan 1, 2004• 25 citations
OpenAlex

Abstract

Abstract. Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single context associated with a particular maximum set of observables can be operationalized, then a context translation principle resolves measurements of different contexts. COUNTERFACTUALS With the rise of quantum mechanics [1, 2, 3, 4] physics proper entered an ancient and sometimes fierce debate in theology and philosophy: the controversy between realism versus idealism. Whereas realism has been subsumed by the proposition that [5] “some entities sometimes exist without being experienced by any finite mind, ” idealism put forward that “we have not the faintest reason for believing in the existence of unexperienced entities. [[Realism]] has been adopted... solely because it simplifies our view of the universe. ” And whereas these issues can be considered nonoperational and thus metaphysical or even ideological, it is also true that they have inspired a great number of minds, to the effect of stimulating new approaches to quantum mechanics, revealing many theoretical details, quantum phenomena and quantum technologies. The Kochen-Specker theorem [6], for example, was motivated from the onset by scholasticism, as in an early programmatic article [7] Ernst Specker related the discussion on the foundations of quantum mechanics to scholastic

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On Counterfactuals and Contextuality

Karl Svozil

Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single context associated with a particular maximum set of observables can be operationalized, then a context translation principle resolves measurements of different contexts.

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The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.

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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.

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Extracontextuality and extravalence in quantum mechanics

Alexia Auffèves, Philippe Grangier

We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

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The present study investigates the tension between objectivism and perspectivism in light of the conceptual and philosophical implications of quantum theory. The guiding dictum of objectivism posits that science reveals the underlying structure of reality independently of human cognitive activity, that is, in terms of mind-independent, discourse-independent properties and relations occurring at any spatiotemporal location. It is shown that objectivism’s stance fits with the applicability of the bivalence principle as the semantic foundation of scientific discourse. It becomes then apparent that the non-Boolean logical structure of quantum theory systematically disrupts the objectivist framework. Along this vein, we provide succinct argumentation demonstrating quantum theory’s affinity to perspectivist reasoning. It is contended that the ubiquitous phenomenon of quantum contextuality, as established by Kochen-Specker’s celebrated theorem, strongly suggests that measurement values of quantum observables can, in general, be regarded as pertaining to an object under investigation only within a local probing frame or perspective from which the object-system is considered. The last remark is reinforced when considered within the endo-theoretic perspectivist framework of quantum mechanics. The essential philosophical meaning of the latter implies the view that the quantum world can be consistently comprehended through a multilevel structure of overlapping Boolean probing frames, realized as locally variable perspectives on a quantum system, being capable of forming jointly a coherent picture of the whole in a nontrivial way. Finally, in the appendix, the endo-theoretic perspectivist framework of quantum theory is critically compared to the relational interpretation of quantum mechanics, particularly in its recent development involving the postulate of “cross-perspective links”, revealing thereby the profoundly different picture of the quantum world’s architecture between the two proposals.

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Quantum Contextuality

Costantino Budroni, Adán Cabello, Otfried Gühne +2 more

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.

•Feb 25, 2021•7 citations
Abstract. Counterfactual reasoning and contextuality is defined and critically evaluated with regard to its nonempirical content. To this end, a uniqueness property of states, explosion views and link observables are introduced. If only a single context associated with a particular maximum set of observables can be operationalized, then a context translation principle resolves measurements of different contexts. COUNTERFACTUALS With the rise of quantum mechanics [1, 2, 3, 4] physics proper entered an ancient and sometimes fierce debate in theology and philosophy: the controversy between realism versus idealism. Whereas realism has been subsumed by the proposition that [5] “some entities sometimes exist without being experienced by any finite mind, ” idealism put forward that “we have not the faintest reason for believing in the existence of unexperienced entities. [[Realism]] has been adopted... solely because it simplifies our view of the universe. ” And whereas these issues can be considered nonoperational and thus metaphysical or even ideological, it is also true that they have inspired a great number of minds, to the effect of stimulating new approaches to quantum mechanics, revealing many theoretical details, quantum phenomena and quantum technologies. The Kochen-Specker theorem [6], for example, was motivated from the onset by scholasticism, as in an early programmatic article [7] Ernst Specker related the discussion on the foundations of quantum mechanics to scholastic
The origin and basis of the notion of quantum contextuality is identified in the Copenhagen approach to quantum mechanics, where context is automatically invoked by its requirement that the experimental arrangement involved in any measurements or set of measurements be taken into account while, in general, the outcome of a measurement may depend on other measurements immediately preceding or jointly performed on the same system. For Bohr, the specification of the experimental situation of any measurement is essential to its significance in light of complementarity and the omnipresence of the quantum of action in physics; for Heisenberg, the incompatibility of pairs of sharp measurements belonging to different situations coheres with both the completeness of the quantum state as an objective physical description and the principle of indeterminacy. Here, context in the Copenhagen approach is taken to be the equivalence class of experimental arrangements corresponding to a set of compatible measurements of quantum observables in standard quantum mechanics; the associated form of contextuality in quantum mechanics arises via the non-commutativity in general of sharp observables, proven by von Neumann, that can appear, providing different contexts. This notion is related to theoretical situations explored later by Bell, by Kochen and Specker, and by others in relation to the classification of hidden-variables theories and elsewhere in physics. This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.
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.
We develop the point of view where quantum mechanics results from the interplay between the quantized number of 'modalities' accessible to a quantum system, and the continuum of 'contexts' that are required to define these modalities. We point out the specific roles of 'extracontextuality' and 'extravalence' of modalities, and relate them to the Kochen-Specker and Gleason theorems.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.
The present study investigates the tension between objectivism and perspectivism in light of the conceptual and philosophical implications of quantum theory. The guiding dictum of objectivism posits that science reveals the underlying structure of reality independently of human cognitive activity, that is, in terms of mind-independent, discourse-independent properties and relations occurring at any spatiotemporal location. It is shown that objectivism’s stance fits with the applicability of the bivalence principle as the semantic foundation of scientific discourse. It becomes then apparent that the non-Boolean logical structure of quantum theory systematically disrupts the objectivist framework. Along this vein, we provide succinct argumentation demonstrating quantum theory’s affinity to perspectivist reasoning. It is contended that the ubiquitous phenomenon of quantum contextuality, as established by Kochen-Specker’s celebrated theorem, strongly suggests that measurement values of quantum observables can, in general, be regarded as pertaining to an object under investigation only within a local probing frame or perspective from which the object-system is considered. The last remark is reinforced when considered within the endo-theoretic perspectivist framework of quantum mechanics. The essential philosophical meaning of the latter implies the view that the quantum world can be consistently comprehended through a multilevel structure of overlapping Boolean probing frames, realized as locally variable perspectives on a quantum system, being capable of forming jointly a coherent picture of the whole in a nontrivial way. Finally, in the appendix, the endo-theoretic perspectivist framework of quantum theory is critically compared to the relational interpretation of quantum mechanics, particularly in its recent development involving the postulate of “cross-perspective links”, revealing thereby the profoundly different picture of the quantum world’s architecture between the two proposals.
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.