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Axioms
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Foundations of Quantum Computing
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Foundations of Quantum Computing

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 14927

Special Issue Editors

Dr. Gustavo Martin Bosyk

E-Mail Website
Guest Editor
1. Instituto de Física La Plata (IFLP), CONICET, UNLP, Diagonal 113 e/63 y 64, 1900 La Plata, Argentina
2. Università degli Studi di Cagliari, I-09123 Cagliari, Italy
Interests: quantum information processing; quantum correlations; uncertainty relations; majorization theory and its applications
Special Issues, Collections and Topics in MDPI journals
Dr. Federico Holik

E-Mail Website
Guest Editor
Instituto de Física La Plata, UNLP, CONICET, Facultad de Ciencias Exactas, La Plata 1900, Argentina
Interests: foundations of quantum mechanics; quantum information theory; quantum probabilities; quantum logic
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The advent of quantum information theory and the possibility of developing quantum computers gave rise to a rich and multidisciplinary field of research, gathering experts from physics, computer science, mathematics and logic. The LoCIC network, that connects experts from different countries of the South American region (for more information, visit the website: http://locic.web.unq.edu.ar/en/), aims to promote academic debate in all areas of quantum information processing, by organizing regular local meetings on the subject open to researchers and students as well. This peer-reviewed Special Issue is part of that effort and is focused in both, the mathematical and physical foundations of quantum computing. Researchers are welcome to present their original and recent developments, as well as review papers, on the topics listed below.

Topics of the Special Issue:

  • Foundations of Quantum Computing
  • Quantum Information Theory
  • Quantum Algorithms
  • Computational Logic
  • Mathematical Logic
  • Lambda Calculus and Type Theory
  • Logical Frameworks
  • Domain Theory and Categorical Models
  • Quantum Communication
  • Quantum Correlations
  • Uncertainty relations
  • Violation of Bell Inequalities
  • Decoherence and Classical Limit
  • Quantum Contextuality
  • Quantum Logic

Dr. Gustavo M. Bosyk
Dr. Federico Holik
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. Axioms 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 2400 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.

Published Papers (5 papers)

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12 pages, 765 KiB  
Article
Impossibility of Quantum Bit Commitment, a Categorical Perspective
by Xin Sun, Feifei He and Quanlong Wang
Axioms 2020, 9(1), 28; https://doi.org/10.3390/axioms9010028 - 09 Mar 2020
Cited by 6 | Viewed by 2639
Abstract
Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to [...] Read more.
Bit commitment is a cryptographic task in which Alice commits a bit to Bob such that she cannot change the value of the bit after her commitment and Bob cannot learn the value of the bit before Alice opens her commitment. According to the Mayers–Lo–Chau (MLC) no-go theorem, ideal bit commitment is impossible within quantum theory. In the information theoretic-reconstruction of quantum theory, the impossibility of quantum bit commitment is one of the three information-theoretic constraints that characterize quantum theory. In this paper, we first provide a very simple proof of the MLC no-go theorem and its quantitative generalization. Then, we formalize bit commitment in the theory of dagger monoidal categories. We show that in the setting of dagger monoidal categories, the impossibility of bit commitment is equivalent to the unitary equivalence of purification. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
12 pages, 364 KiB  
Article
Correlations in Two-Qubit Systems under Non-Dissipative Decoherence
by Diego G. Bussandri, Tristán M. Osán, Pedro W. Lamberti and Ana P. Majtey
Axioms 2020, 9(1), 20; https://doi.org/10.3390/axioms9010020 - 12 Feb 2020
Cited by 1 | Viewed by 1967
Abstract
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states [...] Read more.
We built a new set of suitable measures of correlations for bipartite quantum states based upon a recently introduced theoretical framework [Bussandri et al. in Quantum Inf. Proc. 18:57, 2019]. We applied these measures to examine the behavior of correlations in two-qubit states with maximally mixed marginals independently interacting with non-dissipative decohering environments in different dynamical scenarios of physical relevance. In order to get further insight about the physical meaning of the behavior of these correlation measures we compared our results with those obtained by means of well-known correlation measures such as quantum mutual information and quantum discord. On one hand, we found that the behaviors of total and classical correlations, as assessed by means of the measures introduced in this work, are qualitatively in agreement with the behavior displayed by quantum mutual information and the measure of classical correlations typically used to calculate quantum discord. We also found that the optimization of all the measures of classical correlations depends upon a single parameter and the optimal value of this parameter turns out to be the same in all cases. On the other hand, regarding the measures of quantum correlations used in our studies, we found that in general their behavior does not follow the standard quantum discord D . As the quantification by means of standard quantum discord and the measures of quantum correlations introduced in this work depends upon the assumption that total correlations are additive, our results indicate that this property needs a deeper and systematic study in order to gain a further understanding regarding the possibility to obtain reliable quantifiers of quantum correlations within this additive scheme. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
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14 pages, 436 KiB  
Article
A Quantum Adiabatic Algorithm for Multiobjective Combinatorial Optimization
by Benjamín Barán and Marcos Villagra
Axioms 2019, 8(1), 32; https://doi.org/10.3390/axioms8010032 - 09 Mar 2019
Cited by 1 | Viewed by 3246
Abstract
In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem [...] Read more.
In this work we show how to use a quantum adiabatic algorithm to solve multiobjective optimization problems. For the first time, we demonstrate a theorem proving that the quantum adiabatic algorithm can find Pareto-optimal solutions in finite-time, provided some restrictions to the problem are met. A numerical example illustrates an application of the theorem to a well-known problem in multiobjective optimization. This result opens the door to solve multiobjective optimization problems using current technology based on quantum annealing. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
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10 pages, 379 KiB  
Article
A Logic for Quantum Register Measurements
by Andrea Masini and Margherita Zorzi
Axioms 2019, 8(1), 25; https://doi.org/10.3390/axioms8010025 - 24 Feb 2019
Cited by 4 | Viewed by 3068
Abstract
We know that quantum logics are the most prominent logical systems associated to the lattices of closed Hilbert subspaces. However, what happen if, following a quantum computing perspective, we want to associate a logic to the process of quantum registers measurements? This paper [...] Read more.
We know that quantum logics are the most prominent logical systems associated to the lattices of closed Hilbert subspaces. However, what happen if, following a quantum computing perspective, we want to associate a logic to the process of quantum registers measurements? This paper gives an answer to this question, and, quite surprisingly, shows that such a logic is nothing else that the standard propositional intuitionistic logic. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
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Other

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5 pages, 374 KiB  
Letter
Doily as Subgeometry of a Set of Nonunimodular Free Cyclic Submodules
by Metod Saniga and Edyta Bartnicka
Axioms 2019, 8(1), 28; https://doi.org/10.3390/axioms8010028 - 04 Mar 2019
Viewed by 3227
Abstract
In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the [...] Read more.
In this paper, it is shown that there exists a particular associative ring with unity of order 16 such that the relations between non-unimodular free cyclic submodules of its two-dimensional free left module can be expressed in terms of the structure of the generalized quadrangle of order two. Such a doily-centered geometric structure is surmised to be of relevance for quantum information. Full article
(This article belongs to the Special Issue Foundations of Quantum Computing)
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