Quantum Logics and Quantum Measurements

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Quantum Science and Technology".

Deadline for manuscript submissions: closed (30 June 2022) | Viewed by 3426

Special Issue Editors


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Guest Editor
Department of Computer Science, University of Verona, Verona, Italy
Interests: proof theory; type theory; non-classical logics; quantum computing; lambda calculus

E-Mail Website
Guest Editor
Department of Computer Science, University of Verona, Verona, Italy
Interests: lambda calculus; quantum languages; proof theory; type theory; logics for quantum computing; non-classical logics

Special Issue Information

Dear Colleagues,

One of the great foundational problems of quantum mechanics is the so-called measurement problem. The measurement problem can be considered the starting point of quantum logics that, on the basis of Von Neumann and Birkoff’s pioneering ideas, aims to provide a logical characterization to the measurement process. In more recent years, however, new approaches to quantum logic have been proposed, especially in the research area of quantum computing and more generally of quantum information science. The purpose of this special issue is to take stock of contemporary research on the problem of quantum measurement, both from the foundation of physics point of view (e.g. the alternative theories to the Copenhagen interpretation) and from the formal logical point of view.

The topics of the special issue are:

  • Quantum Logics and the Copenaghen interpretation
  • Quantum Logics and the many worlds interpretation
  • Logics for quantum computing
  • Extensions of quantum logics
  • Proof theory of quantum logics
  • category theories for quantum mechanics/computing
  • modal logics for quantum mechanics/computing.

Prof. Dr. Andrea Masini
Dr. Margherita Zorzi
Guest Editors

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Keywords

  • quantum logics
  • quantum mechanics
  • measurement
  • proof theory
  • non classical logics
  • modal logics

Published Papers (2 papers)

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Research

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15 pages, 308 KiB  
Article
Reasoning about Quantum Information: An Overview of Quantum Dynamic Logic
by Alexandru Baltag and Sonja Smets
Appl. Sci. 2022, 12(9), 4458; https://0-doi-org.brum.beds.ac.uk/10.3390/app12094458 - 28 Apr 2022
Cited by 2 | Viewed by 1242
Abstract
This paper provides an overview of quantum dynamic logics, showing how they have been designed and illustrating how these logics can be applied to verify the correctness of quantum protocols. Similar to the advantages of using dynamic logics to reason about the flow [...] Read more.
This paper provides an overview of quantum dynamic logics, showing how they have been designed and illustrating how these logics can be applied to verify the correctness of quantum protocols. Similar to the advantages of using dynamic logics to reason about the flow of classical information, the quantum analogues of these logics are tailored to the task of reasoning about the flow of quantum information. We present our logical systems in a modular way, starting with the qualitative logic of quantum measurements and unitary evolutions in single quantum systems, which can already express non-classical effects, e.g., the state-changing interference induced by quantum tests, their non-commutativity, etc. We then move on to logics for compound quantum systems that can capture the non-local features of quantum information: separability, entanglement, correlated measurements, Bell states, etc. We then briefly summarize the logic of quantum probabilities and sketch some applications to quantum protocols. Full article
(This article belongs to the Special Issue Quantum Logics and Quantum Measurements)

Review

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22 pages, 426 KiB  
Review
An Introduction to Quantum Model Checking
by Andrea Turrini
Appl. Sci. 2022, 12(4), 2016; https://0-doi-org.brum.beds.ac.uk/10.3390/app12042016 - 15 Feb 2022
Cited by 2 | Viewed by 1538
Abstract
Model checking is a well-established and widely adopted framework used to verify whether a given system satisfies the desired properties. Properties are usually given by means of formulas from a specific logic; there are several logics that can be used, such as CTL [...] Read more.
Model checking is a well-established and widely adopted framework used to verify whether a given system satisfies the desired properties. Properties are usually given by means of formulas from a specific logic; there are several logics that can be used, such as CTL and LTL, which permit the expression of different types of properties on the branching-time or on the linear-time evolution of the system. In this paper, we will consider the problem of model checking quantum systems and present the solutions given in literature for solving such a problem with respect to different types of properties. Full article
(This article belongs to the Special Issue Quantum Logics and Quantum Measurements)
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