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Symmetry
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Symmetries in Quantum Information: Fundamental Aspects and Applications
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Symmetries in Quantum Information: Fundamental Aspects and Applications

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 3488

Special Issue Editors

Prof. Dr. Giacomo D'Ariano

E-Mail Website
Guest Editor
Quit Group, Dipartimento di Fisica, Università degli studi di Pavia, via Bassi 6, 27100 Pavia, Italy
Interests: quantum information; quantum mechanics and foundations of quantum theory
Special Issues, Collections and Topics in MDPI journals
Dr. Alessandro Tosini

E-Mail Website
Guest Editor
QUIT Group, Physics Department, Pavia University, INFN Sezione di Pavia, Via Bassi 6, 27100 Pavia, Italy
Interests: quantum field theory; quantum information; foundations of quantum theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum information, at the intersection of theoretical physics, computer science and mathematics, has opened up new perspectives in all the above fields and in science in general. Now, more then ever, quantum information science is driving technological innovation, boosting high-precision metrology, communication-encrypted protocols and computation algorithms, moving progressively closer to quantum supremacy.

Besides its wide range of applications, quantum information initiated a period of rapid development for the foundations of quantum theory, shedding new light on non-locality, entanglement and complementarity, laying physical grounds for the axioms of quantum theory. To this end, the natural playgrounds of post-quantum theories became popular and formed a common framework for foundational research.

As is the case in all of science, the notion of symmetry has been a guiding principle in the theoretical development of quantum information and recent advances in quantum foundations. It is a powerful mathematical concept which aids in simplifying theoretical derivations and identifying patterns even beyond the quantum.

This Special Issue is intended to further promote the major role that symmetry plays in quantum information, and it is aimed at researchers who are working at the forefront of the diverse areas involved in this interdisciplinary field, ranging from fundamental research to applications and technologies. Authors are welcome to submit original research results as well as review papers presenting their most relevant achievements.

____________________________________________________________________
Distinguished contributing authors:

Bob Coecke
University of Oxford

Carlo Rovelli
AMU Université, Université de Toulon, CNRS, CPT, Marseille, EU

Christopher A. Fuchs
University of Massachusetts Boston

Giulio Chiribella
Department of computer science, the University of Hong Kong

Lucien Hardy
Perimeter Institute for Theoretical Physics

Luis H. Kaufmann
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago

Reinhardt Werner
Theoretical Physics, Leibniz Universität Hannover
____________________________________________________________________

Prof. Giacomo D'Ariano
Dr. Alessandro Tosini
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. Symmetry 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.

Keywords

  • quantum information
  • quantum foundations
  • probabilistic theories
  • quantum computation
  • quantum communications
  • quantum field theory
  • quantum simulations
  • quantum walks and automata

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Published Papers (3 papers)

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Research

24 pages, 3881 KiB  
Article
Parametric Symmetries in Architectures Involving Indefinite Causal Order and Path Superposition for Quantum Parameter Estimation of Pauli Channels
by Francisco Delgado
Symmetry 2023, 15(5), 1097; https://doi.org/10.3390/sym15051097 - 16 May 2023
Cited by 2 | Viewed by 1599
Abstract
Parameter estimation for devices containing or supporting quantum systems is a field of quantum metrology using quantum probe states to reach their characterization. Pauli channels are ideal structures where qubits are transmitted or contained, commonly altering them with specific fingerprints. The ultimate limit [...] Read more.
Parameter estimation for devices containing or supporting quantum systems is a field of quantum metrology using quantum probe states to reach their characterization. Pauli channels are ideal structures where qubits are transmitted or contained, commonly altering them with specific fingerprints. The ultimate limit imposed on such estimation is addressed using the quantum Fisher information, stating a lower bound for it. Although the most simple scheme suggests performing such an estimation directly using the individual channel, other approaches have shown improved outcomes by repeating identical copies of the channel for the characterization, or otherwise those connected inside of specific circuit arrangements. These connections commonly include path superposition or causal indefinite architectures. In addition, other improvements have been observed in concrete channels when complementary unitary controls are included. The current research analyses the complete set of Pauli channels under some of those architectures in a comparative approach to reach a better estimation, thus stating hierarchies. It is observed that the use of those unitary controls notably improves previous outcomes by several orders of magnitude. Full article
(This article belongs to the Special Issue Symmetries in Quantum Information: Fundamental Aspects and Applications)
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26 pages, 324 KiB  
Article
Calculus, Gauge Theory and Noncommutative Worlds
by Louis H. Kauffman
Symmetry 2022, 14(3), 430; https://doi.org/10.3390/sym14030430 - 22 Feb 2022
Cited by 1 | Viewed by 1905
Abstract
This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generalizations of electromagnetism that are related to gauge theory and with the [...] Read more.
This paper shows how gauge theoretic structures arise in a noncommutative calculus where the derivations are generated by commutators. These patterns include Hamilton’s equations, the structure of the Levi–Civita connection, and generalizations of electromagnetism that are related to gauge theory and with the early work of Hermann Weyl. The territory here explored is self-contained mathematically. It is elementary, algebraic, and subject to possible generalizations that are discussed in the body of the paper. Full article
(This article belongs to the Special Issue Symmetries in Quantum Information: Fundamental Aspects and Applications)
33 pages, 481 KiB  
Article
Process Tomography in General Physical Theories
by Giulio Chiribella
Symmetry 2021, 13(11), 1985; https://doi.org/10.3390/sym13111985 - 20 Oct 2021
Cited by 4 | Viewed by 1858
Abstract
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here, we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should [...] Read more.
Process tomography, the experimental characterization of physical processes, is a central task in science and engineering. Here, we investigate the axiomatic requirements that guarantee the in-principle feasibility of process tomography in general physical theories. Specifically, we explore the requirement that process tomography should be achievable with a finite number of auxiliary systems and with a finite number of input states. We show that this requirement is satisfied in every theory equipped with universal extensions, that is, correlated states from which all other correlations can be generated locally with non-zero probability. We show that universal extensions are guaranteed to exist in two cases: (1) theories permitting conclusive state teleportation, and (2) theories satisfying three properties of Causality, Pure Product States, and Purification. In case (2), the existence of universal extensions follows from a symmetry property of Purification, whereby all pure bipartite states with the same marginal on one system are locally interconvertible. Crucially, our results hold even in theories that do not satisfy Local Tomography, the property that the state of any composite system can be identified from the correlations of local measurements. Summarizing, the existence of universal extensions, without any additional requirement of Local Tomography, is a sufficient guarantee for the characterizability of physical processes using a finite number of auxiliary systems and with a finite number of input systems. Full article
(This article belongs to the Special Issue Symmetries in Quantum Information: Fundamental Aspects and Applications)
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