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Probability Theory and Quantum Information
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Probability Theory and Quantum Information

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

Deadline for manuscript submissions: closed (31 October 2025) | Viewed by 2617

Special Issue Editor

Dr. Bin Yan

E-Mail Website
Guest Editor
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Interests: quantum information theory; probability theory--quantum and beyond; statistical physics; quantum foundation

Special Issue Information

Dear Colleagues,

Probability has long been integral to information processing, a fact solidified 80 years ago when Claude Shannon used random codes to transmit information through noisy channels. This concept laid the foundation for modern information theory. More recently, probability has continued to expand its influence into the quantum realm, becoming essential in developing new technologies in quantum information science, such as randomized protocols for quantum computer benchmarking and shadow tomography of quantum states.

On the fundamental level, the role of probability and its interpretations also have profound implications. Questions related to the probabilistic nature of physical systems, such as the measurement problem and the black hole information paradox, remain actively debated. Quantum information science offers fresh perspectives and methods to address these enduring questions.

This Special Issue seeks to gather innovative ideas at the intersection of probability theory and quantum information science. We invite submissions that explore the use of probability theory to address practical problems in quantum information and/or apply insights from quantum information science to address foundational questions in quantum probabilities.

Dr. Bin Yan
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 information
  • probability theory
  • quantum probabilities

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Published Papers (3 papers)

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Research

26 pages, 2220 KB  
Article
Lindbladian Decoherence in Quantum Universal Gates: An Insight Analysis for Digital Noise and Thermalisation
by José Carlos Rebón and Francisco Delgado
Entropy 2025, 27(11), 1089; https://doi.org/10.3390/e27111089 - 22 Oct 2025
Viewed by 582
Abstract
Quantum computing is an emergent field promising the improvement of processing speed in key algorithms by reducing their exponential scaling to polynomial, thus enabling solutions to problems that exceed classical computational capabilities. Gate-based quantum computing is the most common approach but still faces [...] Read more.
Quantum computing is an emergent field promising the improvement of processing speed in key algorithms by reducing their exponential scaling to polynomial, thus enabling solutions to problems that exceed classical computational capabilities. Gate-based quantum computing is the most common approach but still faces high levels of noise and decoherence. Gates play the role of probability mixers codifying information settled in quantum systems. However, they are deviated from their programmed behaviour due to those decoherent effects as a hidden source modifies the desired probability flux. Their quantification of such unavoidable behaviours becomes crucial for quantum error correction or mitigation. This work presents an approach to decoherence in quantum circuits using the Lindblad master equation to model the impact of noise and thermalisation underlying the ideal programmed behaviour expected for processing gates. The Lindblad approach then provides a comprehensive tool to model both probability fluxes being present in the process, thus regarding the gate and the environment. It analyses the deviation of resulting noisy states from the ideal unitary evolution of some gates considered as universal, setting some operating regimes. Thermalisation considers a radiation bath where gates are immersed as a feasible model of decoherence. Numerical simulations track the information loss as a function of the decay rate magnitude. It also exhibits the minimal impact on decoherence coming from particular quantum states being processed, but a higher impact on the number of qubits being processed by the gate. The methodology provides a unified framework to characterise the processing probability transport in quantum gates, including noise or thermalisation effects. Full article
(This article belongs to the Special Issue Probability Theory and Quantum Information)
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22 pages, 3553 KB  
Article
An Extended Epistemic Framework Beyond Probability for Quantum Information Processing with Applications in Security, Artificial Intelligence, and Financial Computing
by Gerardo Iovane
Entropy 2025, 27(9), 977; https://doi.org/10.3390/e27090977 - 18 Sep 2025
Viewed by 590
Abstract
In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum [...] Read more.
In this work, we propose a novel quantum-informed epistemic framework that extends the classical notion of probability by integrating plausibility, credibility, and possibility as distinct yet complementary measures of uncertainty. This enriched quadruple (P, Pl, Cr, Ps) enables a deeper characterization of quantum systems and decision-making processes under partial, noisy, or ambiguous information. Our formalism generalizes the Born rule within a multi-valued logic structure, linking Positive Operator-Valued Measures (POVMs) with data-driven plausibility estimators, agent-based credibility priors, and fuzzy-theoretic possibility functions. We develop a hybrid classical–quantum inference engine that computes a vectorial aggregation of the quadruples, enhancing robustness and semantic expressivity in contexts where classical probability fails to capture non-Kolmogorovian phenomena such as entanglement, contextuality, or decoherence. The approach is validated through three real-world application domains—quantum cybersecurity, quantum AI, and financial computing—where the proposed model outperforms standard probabilistic reasoning in terms of accuracy, resilience to noise, interpretability, and decision stability. Comparative analysis against QBism, Dempster–Shafer, and fuzzy quantum logic further demonstrates the uniqueness of architecture in both operational semantics and practical outcomes. This contribution lays the groundwork for a new theory of epistemic quantum computing capable of modelling and acting under uncertainty beyond traditional paradigms. Full article
(This article belongs to the Special Issue Probability Theory and Quantum Information)
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22 pages, 894 KB  
Article
Quantum Information Supports Delayed Decisions
by Marius Nagy and Naya Nagy
Entropy 2025, 27(9), 894; https://doi.org/10.3390/e27090894 - 23 Aug 2025
Viewed by 817
Abstract
Chatbots, search engines and Database Query Systems are invaluable sources of information for decision-making processes in the data-driven world in which we live today. In this study, we explore the extent to which classical and Quantum Query Systems can support future decisions, taken [...] Read more.
Chatbots, search engines and Database Query Systems are invaluable sources of information for decision-making processes in the data-driven world in which we live today. In this study, we explore the extent to which classical and Quantum Query Systems can support future decisions, taken at a moment where the query service may be inaccessible and the decision has to be based solely on information collected in the past. We show that encoding information at the quantum level allows Query Systems to support future or delayed decisions. More precisely, Grover’s algorithm can be employed in order to extract the desired answer from a large superposition of question–answer pairs obtained through a single interrogation of the system. The method works best for binary answers and can be applied to queries encompassing hundreds or thousands of questions in one query. Extensions are possible if we allow more than one query to be addressed to the system. By comparison, a classical system would require hundreds or thousands of queries in order to offer the same level of support for delayed decisions. Full article
(This article belongs to the Special Issue Probability Theory and Quantum Information)
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