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

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

Deadline for manuscript submissions: closed (1 February 2026) | Viewed by 4420

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; ultrametric 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 (QIP25) is an international conference devoted to quantum foundations—in particular, information and probability, including foundational questions of quantum engineering. This is the 25th conference in the Växjö series. The quantum information revolution has had large, foundational impacts on theoretical and experimental research related to quantum foundations and, more recently, on engineering. For this Special Issue, we invite scholars to submit all kinds of contributions on quantum theory, experiments, and engineering, especially those on foundational questions regarding quantum information, probability, and measurement theories.

Prof. Dr. Andrei Khrennikov
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • quantum foundations
  • quantum probability
  • quantum measurement
  • quantum-like modeling
  • quantum information
  • quantum mechanics
  • quantum decision making
  • quantum cognition
  • quantum biology
  • quantum computers

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Related Special Issues

Published Papers (7 papers)

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Research

36 pages, 441 KB  
Article
Intrinsic Quantization of Linear Hamiltonian Systems
by Luigi Accardi and Carlo Pandiscia
Entropy 2026, 28(4), 384; https://doi.org/10.3390/e28040384 - 31 Mar 2026
Viewed by 168
Abstract
This article discusses the quantization of linear Hamiltonian systems, a historically rich but under explored line of research. The key idea is that a classical linear Hamiltonian system induces on its phase space a compatible complex structure and scalar product, giving rise to [...] Read more.
This article discusses the quantization of linear Hamiltonian systems, a historically rich but under explored line of research. The key idea is that a classical linear Hamiltonian system induces on its phase space a compatible complex structure and scalar product, giving rise to a complex Hilbert space where classical dynamics becomes a one-parameter unitary group. Boson Fock quantization of this group then recovers, up to unitary equivalence, the results of canonical quantization. This expository overview traces the development of this framework from foundational works to modern symplectic perspectives, offering a case study in the dialogue between analysis, geometry, and physics. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
14 pages, 283 KB  
Article
Certified Private Relational Time from Entanglement
by Karl Svozil
Entropy 2026, 28(3), 307; https://doi.org/10.3390/e28030307 - 9 Mar 2026
Viewed by 237
Abstract
We introduce an “entangled clock” in which time is defined operationally by discrete measurement registrations on a singlet state. Locally, each party’s tick rate is fixed by the unbiased marginals. The nontrivial resource is the relational (coincidence-tick) stream: because the singlet’s information budget [...] Read more.
We introduce an “entangled clock” in which time is defined operationally by discrete measurement registrations on a singlet state. Locally, each party’s tick rate is fixed by the unbiased marginals. The nontrivial resource is the relational (coincidence-tick) stream: because the singlet’s information budget is entirely exhausted by joint properties, the only definite temporal structure resides in the correlations between the two parties. Operationally, after exchanging time tags and outcomes, Alice and Bob identify synchronized events (that is, the ++ channel) and thereby obtain a joint tick record. Comparing the ++ coincidence rate R(θ)=P++(a→,b→) to Peres’ isotropic bomb-fragment local-hidden-variable model (yielding Rcl(θ)=θ/(2π)), we find that for obtuse analyzer separations the quantum prediction exceeds this natural classical benchmark, with a maximal relative excess of about 13.6% near θ≈140.5∘. We emphasize that this “faster ticking” refers to the rate of identified coincidence ticks under a specific operational convention, not to an improved local clock rate, precision, or stability. Finally, by using multiple settings and a Bell test, we outline “Certified Private Time”: a device-independent certification of unpredictability/privacy of the relational time-stamp record against adversaries lacking foreknowledge of the settings, analogous to certified randomness generation. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
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24 pages, 356 KB  
Article
Generalization of Bandlimited Functions and Applications to Quantum Probability Distributions
by Leon Cohen
Entropy 2026, 28(2), 198; https://doi.org/10.3390/e28020198 - 10 Feb 2026
Viewed by 294
Abstract
Bandlimited functions are functions whose Fourier transform is confined to a finite band of frequencies. We generalize this concept to representations other than the Fourier transform and show that this leads to a variety of inequalities in arbitrary representations. Several special cases are [...] Read more.
Bandlimited functions are functions whose Fourier transform is confined to a finite band of frequencies. We generalize this concept to representations other than the Fourier transform and show that this leads to a variety of inequalities in arbitrary representations. Several special cases are considered, including frequency, dilation, and the chirplet transform, among others. Examples are given to illustrate each result. We apply the results to quantum mechanical wave functions and probability distributions. For bounded momentum wave functions, we obtain explicit bounds on the position wave function and its derivatives, as well as bounds on the position probability distribution. We also consider the dual problem in which the position wave function is bounded, as in the case of a particle in a box with an arbitrary wave function, and obtain bounds on the corresponding momentum wave function and momentum probability distribution. The case of wave functions that are sums of a finite number of energy eigenfunctions is also developed, and bounds on the associated probability distributions are obtained. A number of specific examples are considered, including a truncated Gaussian wave function and a quantum bump wave function. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
10 pages, 258 KB  
Article
Quantum-like Cognition and Decision-Making: Interpretation of Phases in Quantum-like Superposition
by Andrei Khrennikov
Entropy 2026, 28(2), 134; https://doi.org/10.3390/e28020134 - 23 Jan 2026
Viewed by 561
Abstract
This paper addresses a central conceptual challenge in Quantum-like Cognition and Decision-Making (QCDM) and the broader research program of Quantum-like Modeling (QLM): the interpretation of phases in quantum-like state superpositions. In QLM, system states are represented by normalized vectors in a complex [...] Read more.
This paper addresses a central conceptual challenge in Quantum-like Cognition and Decision-Making (QCDM) and the broader research program of Quantum-like Modeling (QLM): the interpretation of phases in quantum-like state superpositions. In QLM, system states are represented by normalized vectors in a complex Hilbert space, |ψ⟩=∑kXk|k⟩, where the squared amplitudes Pk=|Xk|2 are outcome probabilities. However, the meaning of the phase factors eiϕk in the coefficients Xk=Pkeiϕk has remained elusive, often treating them as purely phenomenological parameters. This practice, while successful in describing cognitive interference effects (the “interference of the mind”), has drawn criticism for expanding the model’s parameter space without a clear physical or cognitive underpinning. Building on a recent framework that connects QCDM to neuronal network activity, we propose a concrete interpretation. We argue that the phases in quantum-like superpositions correspond directly to the phases of random oscillations generated by neuronal circuits in the brain. This interpretation not only provides a natural, non-phenomenological basis for phase parameters within QCDM but also helps to bridge the gap between quantum-like models and classical neurocognitive frameworks, offering a consistent physical analogy for the descriptive power of QLM. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
10 pages, 257 KB  
Article
Kolmogorovian Censorship, Predictive Incompleteness, and the Locality Loophole in Bell Experiments
by Philippe Grangier
Entropy 2026, 28(1), 80; https://doi.org/10.3390/e28010080 - 10 Jan 2026
Viewed by 546
Abstract
We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and [...] Read more.
We revisit the status of quantum probabilities in light of Kolmogorovian Censorship (KC) and the Contexts, Systems, and Modalities (CSM) framework, and we discuss KC-based ideas with respect to superdeterminism, counterfactuality, and predictive incompleteness. After briefly recalling the technical content of KC and its scope, we show that KC correctly identifies that probabilities are classical within a fixed measurement context but does not by itself remove the conceptual tension that motivates nonlocal or conspiratorial explanations of Bell inequality violations. We argue that predictive incompleteness—the view that the quantum state is operationally incomplete until the measurement context is specified—provides a simple, minimal, and explanatory framework that preserves relativistic locality while matching experimental practice. Finally we clarify logical relations among these positions, highlight the assumptions behind them, and justify the move from Kolmogorov’s to Gleason’s framework for quantum probabilities. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
15 pages, 272 KB  
Article
Comprehension as Purification in Reading
by Miho Fuyama
Entropy 2025, 27(12), 1261; https://doi.org/10.3390/e27121261 - 17 Dec 2025
Viewed by 712
Abstract
When reading a novel or poem, readers sometimes gain comprehension or experiences that cannot be expressed in language yet are felt as holistic. Previous studies focused on the linguistically expressible aspects of text comprehension. In this study, we propose a new hypothesis, the [...] Read more.
When reading a novel or poem, readers sometimes gain comprehension or experiences that cannot be expressed in language yet are felt as holistic. Previous studies focused on the linguistically expressible aspects of text comprehension. In this study, we propose a new hypothesis, the purification comprehension hypothesis, that seeks to explain how a reader constructs indescribable and coherent comprehension using quantum probability theory. This hypothesis regards the reading process as purification, in which the reader’s initial interpretation state is mixed, and the reader incorporates external systems, such as the interpretation of other parts of the text or prior knowledge, to purify their state. Therefore, the dimensionality of the state increases and von Neumann entropy decreases through purification. We also highlight two types of reading based on this hypothesis: purification and deterministic. Our model contributes to studies on reading by bridging humanities and scientific studies, provides implications for cognition models that aim to minimize Shannon entropy, and has the potential to apply cognition related to other modalities and media, such as music and art. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
15 pages, 17666 KB  
Article
Multi-Dimensional Quantum-like Resources from Complex Synchronized Networks
by Debadrita Saha and Gregory D. Scholes
Entropy 2025, 27(9), 963; https://doi.org/10.3390/e27090963 - 16 Sep 2025
Viewed by 852
Abstract
Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL states and QL gate operations, which emerge from the dynamics of complex, synchronized networks. The present work extends these ideas to multi-level QL resources, referred to as QL [...] Read more.
Recent publications have introduced the concept of quantum-like (QL) bits, along with their associated QL states and QL gate operations, which emerge from the dynamics of complex, synchronized networks. The present work extends these ideas to multi-level QL resources, referred to as QL dits, as higher-dimensional analogs of QL bits. We employ systems of k-regular graphs to construct QL-dits for arbitrary dimensions, where the emergent eigenspectrum of their adjacency matrices defines the QL-state space. The tensor product structure of multi-QL dit systems is realized through the Cartesian product of graphs. Furthermore, we examine the potential computational advantages of employing d-nary QL systems over two-level QL bit systems, particularly in terms of classical resource efficiency. Overall, this study generalizes the paradigm of using synchronized network dynamics for QL information processing to include higher-dimensional QL resources. Full article
(This article belongs to the Special Issue Quantum Information and Probability: From Foundations to Engineering IV)
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