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Entropy
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Quantum Information and Probability: From Foundations to Engineering II
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Quantum Information and Probability: From Foundations to Engineering II

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Quantum Information".

Deadline for manuscript submissions: closed (31 January 2024) | Viewed by 15254

Special Issue Editor

Prof. Dr. Andrei Khrennikov

E-Mail Website
Guest Editor
International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and social and political sciences; p-adic numbers; p-adic and ultrametric analysis; dynamical systems; p-adic theoretical physics; utrametric models of cognition and psychological behavior; p-adic models in geophysics and petroleum research
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum Information and Probability (QIP23) is an international conference devoted to quantum foundations, in particular, information and probability, including foundational questions of quantum engineering. This is the 23d conference in the Växjö series. The quantum information revolution has large, foundational impacts on theoretical and experimental research related to quantum foundations, and recently also on engineering. We invite all kinds of contributions devoted to quantum theory, experiments, and engineering, and especially to foundational questions with coupling to the quantum information, probability, and measurement theories.

Prof. Dr. Andrei Khrennikov
Guest Editor

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Published Papers (10 papers)

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Research

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49 pages, 468 KiB  
Article
In Our Mind’s Eye: Thinkable and Unthinkable, and Classical and Quantum in Fundamental Physics, with Schrödinger’s Cat Experiment
by Arkady Plotnitsky
Entropy 2024, 26(5), 418; https://doi.org/10.3390/e26050418 - 13 May 2024
Viewed by 1152
Abstract
This article reconsiders E. Schrödinger’s cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as “reality without realism” (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum [...] Read more.
This article reconsiders E. Schrödinger’s cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as “reality without realism” (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum phenomena is beyond conception, an assumption designated as the Heisenberg postulate. Accordingly, in these interpretations, quantum physics is understood in terms of the relationships between what is thinkable and what is unthinkable, with, physical, classical, and quantum, corresponding to thinkable and unthinkable, respectively. The role of classical physics becomes unavoidable in quantum physics, the circumstance designated as the Bohr postulate, which restores to classical physics its position as part of fundamental physics, a position commonly reserved for quantum physics and relativity. This view of quantum physics and relativity is maintained by this article as well but is argued to be sufficient for understanding fundamental physics. Establishing this role of classical physics is a distinctive contribution of the article, which allows it to reconsider Schrödinger’s cat experiment, but has a broader significance for understanding fundamental physics. RWR interpretations have not been previously applied to the cat experiment, including by N. Bohr, whose interpretation, in its ultimate form (he changed it a few times), was an RWR interpretation. The interpretation adopted in this article follows Bohr’s interpretation, based on the Heisenberg and Bohr postulates, but it adds the Dirac postulate, stating that the concept of a quantum object only applies at the time of observation and not independently. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
26 pages, 345 KiB  
Article
Towards Two Bloch Sphere Representation of Pure Two-Qubit States and Unitaries
by Stanislav Filatov and Marcis Auzinsh
Entropy 2024, 26(4), 280; https://doi.org/10.3390/e26040280 - 25 Mar 2024
Cited by 1 | Viewed by 1848
Abstract
We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative [...] Read more.
We extend Bloch sphere formalism to pure two-qubit systems. Combining insights from Geometric Algebra and the analysis of entanglement in different conjugate bases we identify two Bloch sphere geometry that is suitable for representing maximally entangled states. It turns out that the relative direction of the coordinate axes of the two Bloch spheres may be used to describe the states. Moreover, the coordinate axes of one Bloch sphere should be rignt-handed and those of the other one should be left-handed. We describe and depict separable and maximally entangled states as well as entangling and non-entangling rotations. We also offer a graphical representation of the workings of a CNOT gate for different inputs. Finally, we provide a way to also represent partially entangled states and describe entanglement measures related to the surface area of the sphere enclosing the state representation. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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8 pages, 218 KiB  
Article
(Re)Construction of Quantum Space-Time: Transcribing Hilbert into Configuration Space
by Karl Svozil
Entropy 2024, 26(3), 267; https://doi.org/10.3390/e26030267 - 18 Mar 2024
Viewed by 1217
Abstract
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. [...] Read more.
Space-time in quantum mechanics is about bridging Hilbert and configuration space. Thereby, an entirely new perspective is obtained by replacing the Newtonian space-time theater with the image of a presumably high-dimensional Hilbert space, through which space-time becomes an epiphenomenon construed by internal observers. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
24 pages, 684 KiB  
Article
Quantum State Reduction of General Initial States through Spontaneous Unitarity Violation
by Aritro Mukherjee, Srinivas Gotur, Jelle Aalberts, Rosa van den Ende, Lotte Mertens and Jasper van Wezel
Entropy 2024, 26(2), 131; https://doi.org/10.3390/e26020131 - 31 Jan 2024
Cited by 2 | Viewed by 1201
Abstract
The inability of Schrödinger’s unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the [...] Read more.
The inability of Schrödinger’s unitary time evolution to describe the measurement of a quantum state remains a central foundational problem. It was recently suggested that the unitarity of Schrödinger dynamics can be spontaneously broken, resulting in measurement as an emergent phenomenon in the thermodynamic limit. Here, we introduce a family of models for spontaneous unitarity violation that apply to generic initial superpositions over arbitrarily many states, using either single or multiple state-independent stochastic components. Crucially, we show that Born’s probability rule emerges spontaneously in all cases. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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9 pages, 285 KiB  
Article
How Quantum Mechanics Requires Non-Additive Measures
by Gabriele Carcassi and Christine A. Aidala
Entropy 2023, 25(12), 1670; https://doi.org/10.3390/e25121670 - 18 Dec 2023
Viewed by 1637
Abstract
Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ourselves to construct the [...] Read more.
Measure theory is used in physics, not just to capture classical probability, but also to quantify the number of states. In previous works, we found that state quantification plays a foundational role in classical mechanics, and, therefore, we set ourselves to construct the quantum equivalent of the Liouville measure. Unlike the classical counterpart, this quantized measure is non-additive and has a unitary lower bound (i.e., no set of states can have less than one state). Conversely, requiring that state quantification is finite for finite continuous regions and that each state counts as one already implies non-additivity, which in turn implies the failure of classical theory. In this article we show these preliminary results and outline a new line of inquiry that may provide a different insight into the foundations of quantum theory. Additionally, this new approach may prove to be useful to those interested in a quantized theory of space-time, as we believe this requires a quantized measure for the quantification of the independent degrees of freedom. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
26 pages, 381 KiB  
Article
Bild Conception of Scientific Theory Structuring in Classical and Quantum Physics: From Hertz and Boltzmann to Schrödinger and De Broglie
by Andrei Khrennikov
Entropy 2023, 25(11), 1565; https://doi.org/10.3390/e25111565 - 20 Nov 2023
Cited by 1 | Viewed by 1308
Abstract
We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D’Agostino). Following Helmholtz, Hertz established the “Bild conception” for scientific [...] Read more.
We start with a methodological analysis of the notion of scientific theory and its interrelation with reality. This analysis is based on the works of Helmholtz, Hertz, Boltzmann, and Schrödinger (and reviews of D’Agostino). Following Helmholtz, Hertz established the “Bild conception” for scientific theories. Here, “Bild” (“picture”) carries the meaning “model” (mathematical). The main aim of natural sciences is construction of the causal theoretical models (CTMs) of natural phenomena. Hertz claimed that a CTM cannot be designed solely on the basis of observational data; it typically contains hidden quantities. Experimental data can be described by an observational model (OM), often based on the price of acausality. CTM-OM interrelation can be tricky. Schrödinger used the Bild concept to create a CTM for quantum mechanics (QM), and QM was treated as OM. We follow him and suggest a special CTM for QM, so-called prequantum classical statistical field theory (PCSFT). QM can be considered as a PCSFT image, but not as straightforward as in Bell’s model with hidden variables. The common interpretation of the violation of the Bell inequality is criticized from the perspective of the two-level structuring of scientific theories. Such critical analysis of von Neumann and Bell no-go theorems for hidden variables was performed already by De Broglie (and Lochak) in the 1970s. The Bild approach is applied to the two-level CTM-OM modeling of Brownian motion: the overdamped regime corresponds to OM. In classical mechanics, CTM=OM; on the one hand, this is very convenient; on the other hand, this exceptional coincidence blurred the general CTM-OM structuring of scientific theories. We briefly discuss ontic–epistemic structuring of scientific theories (Primas–Atmanspacher) and its relation to the Bild concept. Interestingly, Atmanspacher as well as Hertz claim that even classical physical theories should be presented on the basic of two-level structuring. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
10 pages, 556 KiB  
Article
Large Coherent States Formed from Disordered k-Regular Random Graphs
by Gregory D. Scholes
Entropy 2023, 25(11), 1519; https://doi.org/10.3390/e25111519 - 6 Nov 2023
Cited by 4 | Viewed by 1413
Abstract
The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust [...] Read more.
The present work is motivated by the need for robust, large-scale coherent states that can play possible roles as quantum resources. A challenge is that large, complex systems tend to be fragile. However, emergent phenomena in classical systems tend to become more robust with scale. Do these classical systems inspire ways to think about robust quantum networks? This question is studied by characterizing the complex quantum states produced by mapping interactions between a set of qubits from structure in graphs. We focus on maps based on k-regular random graphs where many edges were randomly deleted. We ask how many edge deletions can be tolerated. Surprisingly, it was found that the emergent coherent state characteristic of these graphs was robust to a substantial number of edge deletions. The analysis considers the possible role of the expander property of k-regular random graphs. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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21 pages, 486 KiB  
Article
Experimental Predictions for Norm-Conserving Spontaneous Collapse
by D. W. Snoke and D. N. Maienshein
Entropy 2023, 25(11), 1489; https://doi.org/10.3390/e25111489 - 27 Oct 2023
Cited by 1 | Viewed by 1118
Abstract
Previous work has shown that nonlocal collapse in quantum mechanics can be described by a deterministic, non-unitary operator added to the standard Schrödinger equation. In terms of key aspects, this term differs from prior work on spontaneous collapse. In this paper, we discuss [...] Read more.
Previous work has shown that nonlocal collapse in quantum mechanics can be described by a deterministic, non-unitary operator added to the standard Schrödinger equation. In terms of key aspects, this term differs from prior work on spontaneous collapse. In this paper, we discuss the possible predictions of this model that can be tested by experiments. This class of collapse model does not intrinsically imply unique experimental predictions, but it allows for the possibility. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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Review

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17 pages, 578 KiB  
Review
Quantum Nonlocality: How Does Nature Do It?
by Marian Kupczynski
Entropy 2024, 26(3), 191; https://doi.org/10.3390/e26030191 - 23 Feb 2024
Cited by 4 | Viewed by 1918
Abstract
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality [...] Read more.
In his article in Science, Nicolas Gisin claimed that quantum correlations emerge from outside space–time. We explainthat they are due to space-time symmetries. This paper is a critical review of metaphysical conclusions found in many recent articles. It advocates the importance of contextuality, Einstein -causality and global symmetries. Bell tests allow only rejecting probabilistic coupling provided by a local hidden variable model, but they do not justify metaphysical speculations about quantum nonlocality and objects which know about each other’s state, even when separated by large distances. The violation of Bell inequalities in physics and in cognitive science can be explained using the notion of Bohr- contextuality. If contextual variables, describing varying experimental contexts, are correctly incorporated into a probabilistic model, then the Bell–CHSH inequalities cannot be proven and nonlocal correlations may be explained in an intuitive way. We also elucidate the meaning of statistical independence assumption incorrectly called free choice, measurement independence or no- conspiracy. Since correlation does not imply causation, the violation of statistical independence should be called contextuality; it does not restrict the experimenter’s freedom of choice. Therefore, contrary to what is believed, closing the freedom-of choice loophole does not close the contextuality loophole. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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18 pages, 274 KiB  
Review
The Ontology of Haag’s Local Quantum Physics
by Gregg Jaeger
Entropy 2024, 26(1), 33; https://doi.org/10.3390/e26010033 - 28 Dec 2023
Cited by 2 | Viewed by 1540
Abstract
The ontology of Local Quantum Physics, Rudolf Haag’s framework for relativistic quantum theory, is reviewed and discussed. It is one of spatiotemporally localized events and unlocalized causal intermediaries, including the elementary particles, which come progressively into existence in accordance with a fundamental arrow [...] Read more.
The ontology of Local Quantum Physics, Rudolf Haag’s framework for relativistic quantum theory, is reviewed and discussed. It is one of spatiotemporally localized events and unlocalized causal intermediaries, including the elementary particles, which come progressively into existence in accordance with a fundamental arrow of time. Haag’s conception of quantum theory is distinguished from others in which events are also central, especially those of Niels Bohr and John Wheeler, with which it has been compared. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering II)
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