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13 pages, 216 KB

Open AccessArticle

Reassessing the Strength of a Class of Wigner’s Friend No-Go Theorems

by Elias Okon

Entropy 2025, 27(6), 563; https://doi.org/10.3390/e27060563 - 27 May 2025

Cited by 1 | Viewed by 670

Two recent, prominent theorems—the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem”—employ so-called extended Wigner’s friend scenarios to try to impose novel, non-trivial constraints on the possible nature of physical reality. While the former is argued to entail that there [...] Read more.

Two recent, prominent theorems—the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem”—employ so-called extended Wigner’s friend scenarios to try to impose novel, non-trivial constraints on the possible nature of physical reality. While the former is argued to entail that there can be no theory in which the results of Wigner and his friend can both be considered objective, the latter is said to place on reality stronger constraints than the Bell and Kochen–Specker theorems. Here, I conduct a thorough analysis of these theorems and show that they suffer from a list of shortcomings that question their validity and limit their strength. I conclude that the “no-go theorem for observer-independent facts” and the “Local Friendliness no-go theorem” fail to impose significant constraints on the nature of physical reality. Full article

(This article belongs to the Section Quantum Information)

9 pages, 261 KB

Open AccessArticle

Chromatic Quantum Contextuality

by Karl Svozil

Entropy 2025, 27(4), 387; https://doi.org/10.3390/e27040387 - 5 Apr 2025

Cited by 3 | Viewed by 639

Abstract

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with n-uniform outcomes per context. Consequently, it [...] Read more.

Chromatic quantum contextuality is a criterion of quantum nonclassicality based on (hyper)graph coloring constraints. If a quantum hypergraph requires more colors than the number of outcomes per maximal observable (context), it lacks a classical realization with n-uniform outcomes per context. Consequently, it cannot represent a “completable” noncontextual set of coexisting n-ary outcomes per maximal observable. This result serves as a chromatic analogue of the Kochen-Specker theorem. We present an explicit example of a four-colorable quantum logic in dimension three. Furthermore, chromatic contextuality suggests a novel restriction on classical truth values, thereby excluding two-valued measures that cannot be extended to n-ary colorings. Using this framework, we establish new bounds for the house, pentagon, and pentagram hypergraphs, refining previous constraints. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness V)

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17 pages, 377 KB

Open AccessArticle

Hidden Variables in Quantum Mechanics from the Perspective of Boltzmannian Statistical Mechanics

by Dustin Lazarovici

Quantum Rep. 2024, 6(3), 465-481; https://doi.org/10.3390/quantum6030031 - 6 Sep 2024

Cited by 1 | Viewed by 2445

Abstract

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum [...] Read more.

This paper examines no-hidden-variables theorems in quantum mechanics from the point of view of statistical mechanics. It presents a general analysis of the measurement process in the Boltzmannian framework that leads to a characterization of (in)compatible measurements and reproduces several features of quantum probabilities often described as “non-classical”. The analysis is applied to versions of the Kochen–Specker and Bell theorems to shed more light on their implications. It is shown how, once the measurement device and the active role of the measurement process are taken into account, contextuality appears as a natural feature of random variables. This corroborates Bell’s criticism that no-go results of the Kochen–Specker type are based on gratuitous assumptions. In contrast, Bell-type theorems are much more profound, but should be understood as nonlocality theorems rather than no-hidden-variables theorems. Finally, the paper addresses misunderstandings and misleading terminology that have confused the debate about hidden variables in quantum mechanics. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports in 2024–2025)

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21 pages, 465 KB

Open AccessEditor’s ChoiceArticle

Generalized Bell Scenarios: Disturbing Consequences on Local-Hidden-Variable Models

by André Mazzari, Gabriel Ruffolo, Carlos Vieira, Tassius Temistocles, Rafael Rabelo and Marcelo Terra Cunha

Entropy 2023, 25(9), 1276; https://doi.org/10.3390/e25091276 - 30 Aug 2023

Cited by 1 | Viewed by 1824

Abstract

Bell nonlocality and Kochen–Specker contextuality are among the main topics in the foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems, while the latter considers a single system. In recent works, [...] Read more.

Bell nonlocality and Kochen–Specker contextuality are among the main topics in the foundations of quantum theory. Both of them are related to stronger-than-classical correlations, with the former usually referring to spatially separated systems, while the latter considers a single system. In recent works, a unified framework for these phenomena was presented. This article reviews, expands, and obtains new results regarding this framework. Contextual and disturbing features inside the local models are explored, which allows for the definition of different local sets with a non-trivial relation among them. The relations between the set of quantum correlations and these local sets are also considered, and post-quantum local behaviours are found. Moreover, examples of correlations that are both local and non-contextual but such that these two classical features cannot be expressed by the same hidden variable model are shown. Extensions of the Fine–Abramsky–Brandenburger theorem are also discussed. Full article

(This article belongs to the Special Issue Quantum Correlations, Contextuality, and Quantum Nonlocality)

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11 pages, 543 KB

Open AccessArticle

Bypassing the Kochen–Specker Theorem: An Explicit Non-Contextual Statistical Model for the Qutrit

by David H. Oaknin

Axioms 2023, 12(1), 90; https://doi.org/10.3390/axioms12010090 - 15 Jan 2023

Cited by 1 | Viewed by 2148

Abstract

We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics, and thus, bypasses the constraints imposed by the Kochen–Specker theorem and its subsequent reformulations. We notice that these renowned theorems crucially rely [...] Read more.

We describe an explicitly non-contextual statistical model of hidden variables for the qutrit, which fully reproduces the predictions of quantum mechanics, and thus, bypasses the constraints imposed by the Kochen–Specker theorem and its subsequent reformulations. We notice that these renowned theorems crucially rely on the implicitly assumed existence of an absolute frame of reference with respect to which physically indistinguishable tests related by spurious gauge transformations can supposedly be assigned well-defined distinct identities. We observe that the existence of such an absolute frame of reference is not required by fundamental physical principles, and hence, assuming it is an unnecessarily restrictive demand. Full article

(This article belongs to the Special Issue Advances in Stochastic Modelling)

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12 pages, 319 KB

Open AccessFeature PaperArticle

Extending Kolmogorov’s Axioms for a Generalized Probability Theory on Collections of Contexts

by Karl Svozil

Entropy 2022, 24(9), 1285; https://doi.org/10.3390/e24091285 - 12 Sep 2022

Cited by 4 | Viewed by 2265

Abstract

Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another [...] Read more.

Kolmogorov’s axioms of probability theory are extended to conditional probabilities among distinct (and sometimes intertwining) contexts. Formally, this amounts to row stochastic matrices whose entries characterize the conditional probability to find some observable (postselection) in one context, given an observable (preselection) in another context. As the respective probabilities need not (but, depending on the physical/model realization, can) be of the Born rule type, this generalizes approaches to quantum probabilities by Aufféves and Grangier, which in turn are inspired by Gleason’s theorem. Full article

(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering)

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21 pages, 413 KB

Open AccessArticle

Quantum Randomness is Chimeric

by Karl Svozil

Entropy 2021, 23(5), 519; https://doi.org/10.3390/e23050519 - 24 Apr 2021

Cited by 4 | Viewed by 4572

Abstract

If quantum mechanics is taken for granted, the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. “Random” quantum events are intimately related to the emergence of both space-time as well as the identification of physical [...] Read more.

If quantum mechanics is taken for granted, the randomness derived from it may be vacuous or even delusional, yet sufficient for many practical purposes. “Random” quantum events are intimately related to the emergence of both space-time as well as the identification of physical properties through which so-called objects are aggregated. We also present a brief review of the metaphysics of indeterminism. Full article

(This article belongs to the Special Issue Noisy Intermediate-Scale Quantum Technologies (NISQ))

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6 pages, 217 KB

Open AccessArticle

Quantum Probability’s Algebraic Origin

by Gerd Niestegge

Entropy 2020, 22(11), 1196; https://doi.org/10.3390/e22111196 - 23 Oct 2020

Cited by 4 | Viewed by 4573

Abstract

Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities [...] Read more.

Max Born’s statistical interpretation made probabilities play a major role in quantum theory. Here we show that these quantum probabilities and the classical probabilities have very different origins. Although the latter always result from an assumed probability measure, the first include transition probabilities with a purely algebraic origin. Moreover, the general definition of transition probability introduced here comprises not only the well-known quantum mechanical transition probabilities between pure states or wave functions, but further physically meaningful and experimentally verifiable novel cases. A transition probability that differs from 0 and 1 manifests the typical quantum indeterminacy in a similar way as Heisenberg’s and others’ uncertainty relations and, furthermore, rules out deterministic states in the same way as the Bell-Kochen-Specker theorem. However, the transition probability defined here achieves a lot more beyond that: it demonstrates that the algebraic structure of the Hilbert space quantum logic dictates the precise values of certain probabilities and it provides an unexpected access to these quantum probabilities that does not rely on states or wave functions. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness II)

24 pages, 2851 KB

Open AccessArticle

A Knot Theoretic Extension of the Bloch Sphere Representation for Qubits in Hilbert Space and Its Application to Contextuality and Many-Worlds Theories

by Stefan Heusler, Paul Schlummer and Malte S. Ubben

Symmetry 2020, 12(7), 1135; https://doi.org/10.3390/sym12071135 - 7 Jul 2020

Cited by 3 | Viewed by 4400

Abstract

We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions

I J K = e^{\frac{2 π i}{2}} = - 1

and [...] Read more.

We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions

I J K = e^{\frac{2 π i}{2}} = - 1

and

J I K = + 1

cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics—in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group. Full article

(This article belongs to the Special Issue The Importance of Being Symmetrical)

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44 pages, 628 KB

Open AccessEditor’s ChoiceReview

What Is So Special about Quantum Clicks?

by Karl Svozil

Entropy 2020, 22(6), 602; https://doi.org/10.3390/e22060602 - 28 May 2020

Cited by 24 | Viewed by 5602

Abstract

This is an elaboration of the “extra” advantage of the performance of quantized physical systems over classical ones, both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based on entities related to (dual) [...] Read more.

This is an elaboration of the “extra” advantage of the performance of quantized physical systems over classical ones, both in terms of single outcomes as well as probabilistic predictions. From a formal point of view, it is based on entities related to (dual) vectors in (dual) Hilbert spaces, as compared to the Boolean algebra of subsets of a set and the additive measures they support. Full article

(This article belongs to the Special Issue Quantum Probability and Randomness II)

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15 pages, 377 KB

Open AccessArticle

Classical Predictions for Intertwined Quantum Observables Are Contingent and Thus Inconclusive

by Karl Svozil

Quantum Rep. 2020, 2(2), 278-292; https://doi.org/10.3390/quantum2020018 - 13 May 2020

Cited by 9 | Viewed by 3732

Abstract

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (also known as gadgets) deliver the strongest form of classical value indefiniteness. However, the [...] Read more.

Classical evaluations of configurations of intertwined quantum contexts induce relations, such as true-implies-false and true-implies-true, but also nonseparability among the input and output terminals. When combined, these exploitable configurations (also known as gadgets) deliver the strongest form of classical value indefiniteness. However, the choice of the respective configuration among all such collections, and thus the relation of its terminals, remains arbitrary and cannot be motivated by some superselection principle inherent to quantum or classical physics. Full article

(This article belongs to the Special Issue Exclusive Feature Papers of Quantum Reports)

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22 pages, 615 KB

Open AccessArticle

New Forms of Quantum Value Indefiniteness Suggest That Incompatible Views on Contexts Are Epistemic

by Karl Svozil

Entropy 2018, 20(6), 406; https://doi.org/10.3390/e20060406 - 24 May 2018

Cited by 11 | Viewed by 4442

Abstract

Extensions of the Kochen–Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single context is epistemic. A remark by Gleason about the ad [...] Read more.

Extensions of the Kochen–Specker theorem use quantum logics whose classical interpretation suggests a true-implies-value indefiniteness property. This can be interpreted as an indication that any view of a quantum state beyond a single context is epistemic. A remark by Gleason about the ad hoc construction of probability measures in Hilbert spaces as a result of the Pythagorean property of vector components is interpreted platonically. Unless there is a total match between preparation and measurement contexts, information about the former from the latter is not ontic, but epistemic. This is corroborated by configurations of observables and contexts with a truth-implies-value indefiniteness property. Full article

(This article belongs to the Special Issue Quantum Foundations: 90 Years of Uncertainty)

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12 pages, 555 KB

Open AccessArticle

The Poincaré Half-Plane for Informationally-Complete POVMs

by Michel Planat

Entropy 2018, 20(1), 16; https://doi.org/10.3390/e20010016 - 31 Dec 2017

Cited by 9 | Viewed by 5422

Abstract

It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from [...] Read more.

It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from the Poincaré upper half-plane model

H

. To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem. Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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22 pages, 314 KB

Open AccessArticle

Contextuality and Indistinguishability

by José Acacio De Barros, Federico Holik and Décio Krause

Entropy 2017, 19(9), 435; https://doi.org/10.3390/e19090435 - 23 Aug 2017

Cited by 16 | Viewed by 4415

Abstract

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, [...] Read more.

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. Full article

(This article belongs to the Special Issue Foundations of Quantum Mechanics)

18 pages, 236 KB

Open AccessEssay

An Order-Theoretic Quantification of Contextuality

by Ian T. Durham

Information 2014, 5(3), 508-525; https://doi.org/10.3390/info5030508 - 22 Sep 2014

Cited by 4 | Viewed by 5485

Abstract

In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous to the sense embodied in the topos-theoretic statement [...] Read more.

In this essay, I develop order-theoretic notions of determinism and contextuality on domains and topoi. In the process, I develop a method for quantifying contextuality and show that the order-theoretic sense of contextuality is analogous to the sense embodied in the topos-theoretic statement of the Kochen–Specker theorem. Additionally, I argue that this leads to a relation between the entropy associated with measurements on quantum systems and the second law of thermodynamics. The idea that the second law has its origin in the ordering of quantum states and processes dates to at least 1958 and possibly earlier. The suggestion that the mechanism behind this relation is contextuality, is made here for the first time. Full article

(This article belongs to the Special Issue Physics of Information)

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