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Entropy
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Quantum Structures and Logics
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Quantum Structures and Logics

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

Deadline for manuscript submissions: closed (31 July 2022) | Viewed by 8266

Special Issue Editors

Prof. Dr. Roberto Leporini

E-Mail Website
Guest Editor
Department of Economics, University of Bergamo, via dei Caniana, 2, I-24127 Bergamo (BG), Italy
Interests: quantum computing; quantum optics; quantum computational structures and logics
Prof. Dr. Roberto Beneduci

E-Mail Website
Guest Editor
Department of Physics, University of Calabria, 87036 Arcavacata, Italy
Interests: quantum mechanics; functional analysis; algebra; general relativity; quantum field theory; probability; solid state physics; nanoelectronics

Special Issue Information

Dear Colleagues,

“Quantum Structures and Logics” is a Special Issue integrating all fields of quantum mechanics and its applications. It provides an important opportunity for researchers to disseminate their results and to obtain feedback from members of the International Quantum Structures Association. Owing to its interdisciplinary and foundational character, the objective is to encourage communication between researchers throughout the world whose research is related to:

  • Quantum structures and their applications in physics, mathematics, and philosophy;
  • Logico-algebraic structures, orthomodular structures, quantum logics, empirical logics, operational structures;
  • Quantum mechanics;
  • Quantum measurements;
  • Quantum computation, quantum information, quantum communication;
  • Philosophy of quantum mechanics;
  • Quantum probability;
  • Interdisciplinary applications of quantum structures.

Prof. Dr. Roberto Leporini
Prof. Dr. Roberto Beneduci
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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 structures
  • quantum logics
  • quantum mechanics
  • quantum computation
  • quantum information

Published Papers (4 papers)

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Research

18 pages, 335 KiB  
Article
A Modal Interpretation of Quantum Spins and Its Application to Freudian Theory
by Giulia Battilotti, Miloš Borozan and Rosapia Lauro Grotto
Entropy 2022, 24(10), 1419; https://doi.org/10.3390/e24101419 - 4 Oct 2022
Cited by 1 | Viewed by 1571
Abstract
In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognition; in doing so, we will show how the [...] Read more.
In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognition; in doing so, we will show how the interplay between formal language and metalanguage allows for characterizing pure quantum states as infinite singletons: in the case of the spin observable, we obtain an equation defining a modality that is then re-interpreted as an abstract projection operator. By including a temporal parameter in the equations and by defining a modal negative operator, we derive an intuitionistic-like negation, for which the non-contradiction law is seen as an equivalent of the quantum uncertainty. Building on the psychoanalytic theory of Bi-Logic by Matte Blanco, we use modalities in interpreting the emergence of conscious representations from an unconscious one, and we demonstrate that this description fits well with Freud’s view of the role of negation in mental processes. Psychoanalysis, where affect plays a prominent role in shaping not only conscious, but also unconscious representations, is therefore seen as a suitable model to expand the domain of quantum cognition to the broader field of affective quantum cognition. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
27 pages, 1656 KiB  
Article
Human Perception as a Phenomenon of Quantization
by Diederik Aerts and Jonito Aerts Arguëlles
Entropy 2022, 24(9), 1207; https://doi.org/10.3390/e24091207 - 29 Aug 2022
Cited by 6 | Viewed by 2586
Abstract
For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of ‘categorical perception’ has put us on track to find a possible [...] Read more.
For two decades, the formalism of quantum mechanics has been successfully used to describe human decision processes, situations of heuristic reasoning, and the contextuality of concepts and their combinations. The phenomenon of ‘categorical perception’ has put us on track to find a possible deeper cause of the presence of this quantum structure in human cognition. Thus, we show that in an archetype of human perception consisting of the reconciliation of a bottom up stimulus with a top down cognitive expectation pattern, there arises the typical warping of categorical perception, where groups of stimuli clump together to form quanta, which move away from each other and lead to a discretization of a dimension. The individual concepts, which are these quanta, can be modeled by a quantum prototype theory with the square of the absolute value of a corresponding Schrödinger wave function as the fuzzy prototype structure, and the superposition of two such wave functions accounts for the interference pattern that occurs when these concepts are combined. Using a simple quantum measurement model, we analyze this archetype of human perception, provide an overview of the experimental evidence base for categorical perception with the phenomenon of warping leading to quantization, and illustrate our analyses with two examples worked out in detail. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
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20 pages, 382 KiB  
Article
Quantum Models à la Gabor for the Space-Time Metric
by Gilles Cohen-Tannoudji, Jean-Pierre Gazeau, Célestin Habonimana and Juma Shabani
Entropy 2022, 24(6), 835; https://doi.org/10.3390/e24060835 - 16 Jun 2022
Cited by 2 | Viewed by 1590
Abstract
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space x,k into Hilbertian operators. The x=xμ values are space-time variables, and the k=kμ [...] Read more.
As an extension of Gabor signal processing, the covariant Weyl-Heisenberg integral quantization is implemented to transform functions on the eight-dimensional phase space x,k into Hilbertian operators. The x=xμ values are space-time variables, and the k=kμ values are their conjugate frequency-wave vector variables. The procedure is first applied to the variables x,k and produces essentially canonically conjugate self-adjoint operators. It is next applied to the metric field gμν(x) of general relativity and yields regularized semi-classical phase space portraits gˇμν(x). The latter give rise to modified tensor energy density. Examples are given with the uniformly accelerated reference system and the Schwarzschild metric. Interesting probabilistic aspects are discussed. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
22 pages, 377 KiB  
Article
Quantum Uncertainties and Holism Seem to Render Irrelevant Qudit-Semantics
by Roberto Leporini
Entropy 2021, 23(6), 735; https://doi.org/10.3390/e23060735 - 10 Jun 2021
Cited by 1 | Viewed by 1433
Abstract
We consider a semantics based on the peculiar holistic features of the quantum formalism. Any formula of the language gives rise to a quantum circuit that transforms the density operator associated to the formula into the density operator associated to the atomic subformulas [...] Read more.
We consider a semantics based on the peculiar holistic features of the quantum formalism. Any formula of the language gives rise to a quantum circuit that transforms the density operator associated to the formula into the density operator associated to the atomic subformulas in a reversible way. The procedure goes from the whole to the parts against the compositionality-principle and gives rise to a semantic characterization for a new form of quantum logic that has been called “Łukasiewicz quantum computational logic”. It is interesting to compare the logic based on qubit-semantics with that on qudit-semantics. Having in mind the relationships between classical logic and Łukasiewicz-many valued logics, one could expect that the former is stronger than the fragment of the latter. However, this is not the case. From an intuitive point of view, this can be explained by recalling that the former is a very weak form of logic. Many important logical arguments, which are valid either in Birkhoff and von Neumann’s quantum logic or in classical logic, are generally violated. Full article
(This article belongs to the Special Issue Quantum Structures and Logics)
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