On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

Feintzeig, Benjamin H.; Fletcher, Samuel C.

doi:10.1007/s10701-017-0061-z

Cited by 9 publications

(29 citation statements)

References 75 publications

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“…in decision making and artificial intelligence [29]. Recently it was applied for describing aspects of the Bell's inequality [33][34][35]. The quantum imprecise probability is to be sought independently, along the physical arguments.…”

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confidence: 99%

Excluding joint probabilities from quantum theory

Allahverdyan

Danageozian

2018

Phys. Rev. A

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Quantum theory does not provide a unique definition for the joint probability of two noncommuting observables, which is the next important question after the Born's probability for a single observable. Instead, various definitions were suggested, e.g. via quasi-probabilities or via hidden-variable theories. After reviewing open issues of the joint probability, we relate it to quantum imprecise probabilities, which are non-contextual and are consistent with all constraints expected from a quantum probability. We study two non-commuting observables in a two-dimensional Hilbert space and show that there is no precise joint probability that applies for any quantum state and is consistent with imprecise probabilities. This contrasts to theorems by Bell and Kochen-Specker that exclude joint probabilities for more than two non-commuting observables, in Hilbert space with dimension larger than two. If measurement contexts are included into the definition, joint probabilities are not anymore excluded, but they are still constrained by imprecise probabilities.

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confidence: 99%

Excluding joint probabilities from quantum theory

Allahverdyan

Danageozian

2018

Phys. Rev. A

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“…In particular, our map sends strongly contextual empirical models (such as the Kochen-Specker model) to WPSs that maximally violate subadditivity, logically contextual empirical models (such as the Hardy model) to WPSs that violate subadditivity, and probabilistically contextual empirical models (such as the Bell model) to WPSs that violate additivity. This result then allows us to resolve the puzzle about why the Dutch Bookability that appears in (Feintzeig 2015;Feintzeig and Fletcher 2017) is so dramatic: Kochen-Specker models are not the only kind of quantum models giving rise to Dutch Books; other (Standard) models such as the Hardy and Bell models do so as well. However, Kochen-Specker models result in such a dramatic form of Dutch Bookability precisely because they witness the strongest form of contextuality.…”

Section: Our Motivation and Resultsmentioning

confidence: 95%

“…A further motivation for pursuing our topic is to provide an explanation of why the particular kind of Dutch Bookability that appears in (Feintzeig 2015;Feintzeig and Fletcher 2017) stems from such a dramatic violation of additivity, in which the sample space is covered by a finite number of measure zero sets. Why should the Dutch Books of quantum theory be so extreme?…”

Section: Our Motivation and Resultsmentioning

confidence: 99%

“…In the next subsection, we explain how the structural features that allow us to define this hierarchy can be represented within the WPS framework. Feintzeig and Fletcher (2017) assume that Generalized HVTs (GHVTs) will at least have the structure of a Weak Probability Space (WPS). Thus, in order to demonstrate that GHVTs are Dutch Bookable, they provide a method of representing a quantum Kochen-Specker model within the WPS framework.…”

Section: Gluing Inconsistency: Empirical Modelsmentioning

confidence: 99%

“…In this final section, we turn to a partial evaluation of whether formal Dutch Bookability can be used to provide a normative argument against GHVTs. Feintzeig and Fletcher (2017) seek to use (Dutch) arguments to demonstrate that the probabilities of hidden variable theories based on WPSs-which we have labeled GHVTs-cannot be given a 'rational' subjective intepretation. To unpack this claim, first recall that the existence of a 'finite null cover' constitutes a maximal violation of subadditivity, the strongest rung of the Dutch Bookability hierarchy (pictured in Figure 4.2).…”

Section: Is Dutch Bookability Normative?mentioning

confidence: 99%

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Two Forms of Inconsistency in Quantum Foundations

Steeger

Teh

2021

The British Journal for the Philosophy of Science

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Abstract Recently, there has been some discussion of how Dutch book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig [2015]; Feintzeig and Fletcher [2017]; Wroński and Godziszewski [2017]). In this paper, we argue that the ‘form of inconsistency’ underlying this alleged irrationality is deeply and comprehensively related to the more familiar ‘inconsistency’ phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger ([2011]) corresponds to a hierarchy of additivity/convexity-violations that yields formal Dutch books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch books can be given a convincing normative interpretation. 1Introduction2Contextuality and Inconsistency2.1Contextuality2.2Gluing inconsistency2.3Dutch bookability2.4Our motivation and results3Representing Empirical Models3.1Gluing inconsistency: empirical models3.2Weak probability spaces: representations of empirical models4The Hierarchies4.1Contextuality and additivity-violation4.2Dutch bookability and convexity-violation5Is Dutch Bookability Normative?

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Contextuality, Fine-Tuning and Teleological Explanation

Adlam

2021

Found Phys

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I assess various proposals for the source of the intuition that there is something problematic about contextuality, ultimately concluding that contextuality is best thought of in terms of fine-tuning. I then argue that as with other fine-tuning problems in quantum mechanics, this behaviour can be understood as a manifestation of teleological features of physics. Finally I discuss several formal mathematical frameworks that have been used to analyse contextuality and consider how their results should be interpreted by scientific realists. In the course of this discussion I obtain several new mathematical results-I demonstrate that preparation contextuality is a form of fine-tuning, I show that measurement contextuality can be explained by appeal to a global constraint forbidding closed causal loops, and I demonstrate how negative probabilities can arise from a classical ontological model together with an epistemic restriction.

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On Noncontextual, Non-Kolmogorovian Hidden Variable Theories

Cited by 9 publications

References 75 publications

Excluding joint probabilities from quantum theory

Excluding joint probabilities from quantum theory

Two Forms of Inconsistency in Quantum Foundations

Contextuality, Fine-Tuning and Teleological Explanation

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