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Symmetry
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Measurements in Quantum Mechanics
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Measurements in Quantum Mechanics

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

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 13839

Special Issue Editor

Prof. Dr. Krzysztof Urbanowski

E-Mail Website
Guest Editor
Institute of Physics, University of Zielona Gora, Licealna 9, 65-417 Zielona Gora, Poland
Interests: quantum theory; problem of quantum measurements; unstable states; decaying dark energy

Special Issue Information

Dear Colleagues,

The problem of measurements in quantum mechanics is as old as the modern concept of quantum mechanics. Understanding of quantum mechanics is impossible without understanding what measurement is in quantum mechanics and how measurement is defined. These questions are a basic part of the problem of interpretation in quantum mechanics. A discussion on how to interpret the results of measurements is very old: Here, one should mention the Bohr–Einstein debates, out of which both the Einstein–Podolsky–Rosen (EPR) and Schrödinger’s cat paradoxes resulted. These interpretation problems were the result of an apparent conflict between several principles of the quantum theory of measurement. A related question is what the relationship will be between the measurement results of two different observables that lead to the uncertainty relations. In general, the measurement problem is not simply an internal interpretative problem of quantum mechanics but also an inspiration for theoretical and experimental research and philosophical debate. The range of topics for research is very broad: the von Neumann model of ideal measurements, quantum models of the measurement process, single measurements (destructive or not), many successive measurements including continuous measurements (quantum Zeno and anti-Zeno effects), the so-called weak measurements, uncertainty relations (including entropic and generalized), experiments with measurements of an individual atomic particle (quantum dots, quantum traps, and related problems), single-slit diffraction experiments, and others.

This Special Issue is devoted to the broad range of topics which are related to the problem of measurement in quantum mechanics. I would like to invite all colleagues to submit their original research results, reviews, and short communication articles to this issue. Both theoretical and experimental proposals are welcome.

Prof. Dr. Krzysztof Urbanowski
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 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

  • ideal and non-ideal measurements
  • models of the measurement process
  • quantum Zeno and anti-Zeno effects
  • weak measurements
  • quantum entanglement and steering
  • EPR correlations
  • uncertainty relations
  • experiments searching properties of individual quantum objects

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Published Papers (6 papers)

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Editorial

Jump to: Research

2 pages, 176 KiB  
Editorial
Editorial Conclusion for the Special Issue “Measurements in Quantum Mechanics”
by Krzysztof Urbanowski
Symmetry 2023, 15(1), 111; https://doi.org/10.3390/sym15010111 - 31 Dec 2022
Viewed by 1049
Abstract
This Special Issue is devoted to the broad range of topics related to the problem of quantum measurements, which is as old as the modern concept of quantum mechanics [...] Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)

Research

Jump to: Editorial

19 pages, 598 KiB  
Article
Comparing Hermitian and Non-Hermitian Quantum Electrodynamics
by Jake Southall, Daniel Hodgson, Robert Purdy and Almut Beige
Symmetry 2022, 14(9), 1816; https://doi.org/10.3390/sym14091816 - 1 Sep 2022
Cited by 3 | Viewed by 2709
Abstract
In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator [...] Read more.
In recent years, non-Hermitian quantum physics has gained a great deal of popularity in the quantum optics and condensed matter communities in order to model quantum systems with varying symmetries. In this paper, we identify a non-standard inner product that implies bosonic commutator relations for local electric and magnetic field observables and leads to a natural local biorthogonal description of the quantised electromagnetic field. When comparing this description with an alternative local Hermitian description, in which the states of local photonic particles, i.e., of so-called bosons localised in position (blips), are orthogonal under the conventional Hermitian inner product, we find that there is an equivalence between the two approaches. Careful consideration needs to be given to the physical interpretation of the different descriptions. Whether a Hermitian or a non-Hermitian approach is more suitable depends on the circumstances that we want to model. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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10 pages, 342 KiB  
Article
Coherence Trapping in Open Two-Qubit Dynamics
by Mariam Algarni, Kamal Berrada, Sayed Abdel-Khalek and Hichem Eleuch
Symmetry 2021, 13(12), 2445; https://doi.org/10.3390/sym13122445 - 17 Dec 2021
Cited by 4 | Viewed by 2316
Abstract
In this manuscript, we examine the dynamical behavior of the coherence in open quantum systems using the l1 norm. We consider a two-qubit system that evolves in the framework of Kossakowski-type quantum dynamical semigroups (KTQDSs) of completely positive maps (CPMs). We find [...] Read more.
In this manuscript, we examine the dynamical behavior of the coherence in open quantum systems using the l1 norm. We consider a two-qubit system that evolves in the framework of Kossakowski-type quantum dynamical semigroups (KTQDSs) of completely positive maps (CPMs). We find that the quantum coherence can be asymptotically maintained with respect to the values of the system parameters. Moreover, we show that the quantum coherence can resist the effect of the environment and preserve even in the regime of long times. The obtained results also show that the initially separable states can provide a finite value of the coherence during the time evolution. Because of such properties, several states in this type of environments are good candidates for incorporating quantum information and optics (QIO) schemes. Finally, we compare the dynamical behavior of the coherence with the entire quantum correlation. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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12 pages, 975 KiB  
Article
Quantum Steering in Two- and Three-Mode ??-Symmetric Systems
by Vinh Le Duc, Joanna K. Kalaga, Wiesław Leoński, Mateusz Nowotarski, Konrad Gruszka and Małgorzata Kostrzewa
Symmetry 2021, 13(11), 2201; https://doi.org/10.3390/sym13112201 - 18 Nov 2021
Cited by 4 | Viewed by 1901
Abstract
We consider two PT-symmetric models, consisting of two or three single-mode cavities. In both models, the cavities are coupled to each other by linear interactions, forming a linear chain. Additionally, the first and last of such cavities interact with an environment. Since [...] Read more.
We consider two PT-symmetric models, consisting of two or three single-mode cavities. In both models, the cavities are coupled to each other by linear interactions, forming a linear chain. Additionally, the first and last of such cavities interact with an environment. Since the models are PT-symmetric, they are described by non-Hermitian Hamiltonians that, for a specific range of system parameters, possess real eigenvalues. We show that in the models considered in the article, the steering generation process strongly depends on the coupling strengths and rates of the gains/losses in energy. Moreover, we find the values of parameters describing the system for which the steering appears. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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30 pages, 13027 KiB  
Article
The Topological Origin of Quantum Randomness
by Stefan Heusler, Paul Schlummer and Malte S. Ubben
Symmetry 2021, 13(4), 581; https://doi.org/10.3390/sym13040581 - 1 Apr 2021
Cited by 5 | Viewed by 2783
Abstract
What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for [...] Read more.
What is the origin of quantum randomness? Why does the deterministic, unitary time development in Hilbert space (the ‘4π-realm’) lead to a probabilistic behaviour of observables in space-time (the ‘2π-realm’)? We propose a simple topological model for quantum randomness. Following Kauffmann, we elaborate the mathematical structures that follow from a distinction(A,B) using group theory and topology. Crucially, the 2:1-mapping from SL(2,C) to the Lorentz group SO(3,1) turns out to be responsible for the stochastic nature of observables in quantum physics, as this 2:1-mapping breaks down during interactions. Entanglement leads to a change of topology, such that a distinction between A and B becomes impossible. In this sense, entanglement is the counterpart of a distinction (A,B). While the mathematical formalism involved in our argument based on virtual Dehn twists and torus splitting is non-trivial, the resulting haptic model is so simple that we think it might be suitable for undergraduate courses and maybe even for High school classes. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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9 pages, 344 KiB  
Article
Entanglement of General Two-Qubit States in a Realistic Framework
by Sayed Abdel-Khalek, Kamal Berrada, Eied M. Khalil and Fadhel Almalki
Symmetry 2021, 13(3), 386; https://doi.org/10.3390/sym13030386 - 27 Feb 2021
Cited by 1 | Viewed by 2062
Abstract
In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new [...] Read more.
In the present paper, we examine the quantum entanglement for more general states of two-qubit system in the context of spin coherent states (SCSs). We consider the concurrence as a quantifier of entanglement and express it in terms of SCSs. We determine new set of maximally entangled conditions that provide the maximal amount of entanglement for certain values of the amplitudes of SCSs for the case of pure states. Finally, we examine the entanglement of a class of mixed states of the two qubits and provide the range in which the entanglement value is maximal with respect to the values of the amplitudes of SCSs. Full article
(This article belongs to the Special Issue Measurements in Quantum Mechanics)
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