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Special Issue "Quantum Mechanics: From Foundations to Information Technologies"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: 1 February 2018

Special Issue Editors

Guest Editor
Prof. Dr. Giacomo Mauro D'Ariano

QUit Group, Department of Physics, University of Pavia, I-27100 Pavia, Italy
Website | E-Mail
Phone: +39 0382 987 484
Fax: +39 0382 987 793
Interests: quantum information; foundations of quantum physics; foundations of quantum field theory; tension between quantum theory and general relativity
Guest Editor
Prof. Dr. Andrei Khrennikov

International Center for Mathematical Modeling in Physics, Engineering, Economics, and Cognitive Science, Linnaeus University, S-35195, Växjö, Sweden
Website | E-Mail
Interests: quantum foundations, information, probability, contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, social and political sciences; p-adic numbers, p-adic and ultrametric analysis, dynamical systems, p-adic theoretical physics, utrametric models of cognition and psychological behavior, p-adic models in geophysics and petroleum research
Guest Editor
Prof. Dr. Massimo Melucci

Department of Information Engineering, University of Padua, 35131 Padova, Italy
Website | E-Mail
Interests: application of the mathematical formalism of quantum theory for information retrieval

Special Issue Information

Dear Colleagues,

The last years have been characterized by a tremendous development of quantum technologies and related theoretical studies. In particular, the EU recently launched quantum technologies as a flagship. It was pointed out in an EU manifesto that “Quantum theory which was developed in the early 1900s by Plank, Bohr, Feynman and Einstein has fundamentally changed our understanding of how light and matter behave at extremely small scales. Our ability to manipulate quantum effects in customised systems and materials is now paving the way for a second quantum revolution.” One can speak about the second quantum revolution: The revolutionary transformation of quantum physics in the informational framework. 

At the same time, the foundational basis of this revolution is still not concrete and contains a few sandy and shaky slices. Therefore, the studies in quantum foundations nowadays are not less (but may be even more) important than 100 years ago when quantum mechanics was born.

The aim of the present Special Issue is to critically analyze the foundational basis of quantum mechanics in the light of recent developments in quantum information and probability and the establishment of quantum informational technologies.

We mention a few possible topics:

  • Foundations of quantum information theory
  • Information approach to quantum foundations, information based derivations of quantum mechanics
  • Quantum measurement problem
  • Critical analysis of the foundational basis of quantum technologies, quantum computing, quantum cryptography, and quantum random generators
  • Foundations of quantum probability theory
  • Generalized probabilistic models
  • Quantum contextuality and generalized contextual models
  • Quantum versus classical randomness and quantum random generators
  • Experimental studies related to quantum foundations and quantum technologies
  • Applications of the quantum formalism outside of physics: From molecular biology to cognition, decision making, sociology, economics, finances and politics.
  • Information retrieval and quantum methods, theory and concrete applications
  • Entanglement: Theory and experiment
  • Bell inequality: Theory and experiment
  • Quantum nonlocality: Theory and experiment
  • Mathematical foundations of quantum mechanics

Of course, possible topics need not be restricted to the listed above; any contribution directed to improvement of quantum foundations, development of quantum information theory and their technological applications is very welcome. 

This Special Issue will also collect a limited number of selected talks or articles presented at the 2017 Foundations of Quantum Mechanics and Technology (FQMT) (https://lnu.se/en/fqmt/).

Prof. Dr. Giacomo Mauro D'Ariano
Prof. Dr. Andrei Khrennikov
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 papers will be 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 1500 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 (6 papers)

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Research

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Open AccessArticle Quantum Minimum Distance Classifier
Entropy 2017, 19(12), 659; doi:10.3390/e19120659
Received: 15 October 2017 / Revised: 21 November 2017 / Accepted: 29 November 2017 / Published: 1 December 2017
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Abstract
We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named
[...] Read more.
We propose a quantum version of the well known minimum distance classification model called Nearest Mean Classifier (NMC). In this regard, we presented our first results in two previous works. First, a quantum counterpart of the NMC for two-dimensional problems was introduced, named Quantum Nearest Mean Classifier (QNMC), together with a possible generalization to any number of dimensions. Secondly, we studied the n-dimensional problem into detail and we showed a new encoding for arbitrary n-feature vectors into density operators. In the present paper, another promising encoding is considered, suggested by recent debates on quantum machine learning. Further, we observe a significant property concerning the non-invariance by feature rescaling of our quantum classifier. This fact, which represents a meaningful difference between the NMC and the respective quantum version, allows us to introduce a free parameter whose variation provides, in some cases, better classification results for the QNMC. The experimental section is devoted: (i) to compare the NMC and QNMC performance on different datasets; and (ii) to study the effects of the non-invariance under uniform rescaling for the QNMC. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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Open AccessArticle Coherent Processing of a Qubit Using One Squeezed State
Entropy 2017, 19(12), 653; doi:10.3390/e19120653
Received: 5 October 2017 / Revised: 19 November 2017 / Accepted: 22 November 2017 / Published: 30 November 2017
PDF Full-text (260 KB) | HTML Full-text | XML Full-text
Abstract
In a departure from most work in quantum information utilizing Gaussian states, we use a single such state to represent a qubit and model environmental noise with a class of quadratic dissipative equations. A benefit of this single Gaussian representation is that with
[...] Read more.
In a departure from most work in quantum information utilizing Gaussian states, we use a single such state to represent a qubit and model environmental noise with a class of quadratic dissipative equations. A benefit of this single Gaussian representation is that with one deconvolution, we can eliminate noise. In this deconvolution picture, a basis of squeezed states evolves to another basis of such states. One of the limitations of our approach is that noise is eliminated only at a privileged time. We suggest that this limitation may actually be used advantageously to send information securely: the privileged time is only known to the sender and the receiver, and any intruder accessing the information at any other time encounters noisy data. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
Open AccessArticle “Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia
Entropy 2017, 19(10), 513; doi:10.3390/e19100513
Received: 1 September 2017 / Revised: 19 September 2017 / Accepted: 21 September 2017 / Published: 24 September 2017
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Abstract
Werner Heisenberg introduced the notion of quantum potentia in order to accommodate the indeterminism associated with quantum measurement. Potentia captures the capacity of the system to be found to possess a property upon a corresponding sharp measurement in which it is actualized. The
[...] Read more.
Werner Heisenberg introduced the notion of quantum potentia in order to accommodate the indeterminism associated with quantum measurement. Potentia captures the capacity of the system to be found to possess a property upon a corresponding sharp measurement in which it is actualized. The specific potentiae of the individual system are represented formally by the complex amplitudes in the measurement bases of the eigenstate in which it is prepared. All predictions for future values of system properties can be made by an experimenter using the probabilities which are the squared moduli of these amplitudes that are the diagonal elements of the density matrix description of the pure ensemble to which the system, so prepared, belongs. Heisenberg considered the change of the ensemble attribution following quantum measurement to be analogous to the classical change in Gibbs’ thermodynamics when measurement of the canonical ensemble enables a microcanonical ensemble description. This analogy, presented by Heisenberg as operating at the epistemic level, is analyzed here. It has led some to claim not only that the change of the state in measurement is classical mechanical, bringing its quantum character into question, but also that Heisenberg held this to be the case. Here, these claims are shown to be incorrect, because the analogy concerns the change of ensemble attribution by the experimenter upon learning the result of the measurement, not the actualization of the potentia responsible for the change of the individual system state which—in Heisenberg’s interpretation of quantum mechanics—is objective in nature and independent of the experimenter’s knowledge. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
Open AccessArticle Extraction of the Proton and Electron Radii from Characteristic Atomic Lines and Entropy Principles
Entropy 2017, 19(7), 293; doi:10.3390/e19070293
Received: 13 April 2017 / Revised: 8 June 2017 / Accepted: 9 June 2017 / Published: 29 June 2017
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Abstract
We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of
[...] Read more.
We determine the proton and electron radii by analyzing constructive resonances at minimum entropy for elements with atomic number Z ≥ 11.We note that those radii can be derived from entropy principles and published photoelectric cross sections data from the National Institute of Standards and Technology (NIST). A resonance region with optimal constructive interference is given by a principal wavelength λ of the order of Bohr atom radius. Our study shows that the proton radius deviations can be measured. Moreover, in the case of the electron, its radius converges to electron classical radius with a value of 2.817 fm. Resonance waves afforded us the possibility to measure the proton and electron radii through an interference term. This term, was a necessary condition in order to have an effective cross section maximum at the threshold. The minimum entropy means minimum proton shape deformation and it was found to be (0.830 ± 0.015) fm and the average proton radius was found to be (0.825 − 0.0341; 0.888 + 0.0405) fm. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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Open AccessArticle A Functorial Construction of Quantum Subtheories
Entropy 2017, 19(5), 220; doi:10.3390/e19050220
Received: 2 March 2017 / Revised: 3 May 2017 / Accepted: 4 May 2017 / Published: 11 May 2017
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Abstract
We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom,
[...] Read more.
We apply the geometric quantization procedure via symplectic groupoids to the setting of epistemically-restricted toy theories formalized by Spekkens (Spekkens, 2016). In the continuous degrees of freedom, this produces the algebraic structure of quadrature quantum subtheories. In the odd-prime finite degrees of freedom, we obtain a functor from the Frobenius algebra of the toy theories to the Frobenius algebra of stabilizer quantum mechanics. Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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Other

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Open AccessLetter A Combinatorial Grassmannian Representation of the Magic Three-Qubit Veldkamp Line
Entropy 2017, 19(10), 556; doi:10.3390/e19100556
Received: 17 September 2017 / Revised: 13 October 2017 / Accepted: 17 October 2017 / Published: 19 October 2017
PDF Full-text (235 KB) | HTML Full-text | XML Full-text
Abstract
It is demonstrated that the magic three-qubit Veldkamp line occurs naturally within the Veldkamp space of a combinatorial Grassmannian of type G2(7), V(G2(7)). The lines of the ambient symplectic polar
[...] Read more.
It is demonstrated that the magic three-qubit Veldkamp line occurs naturally within the Veldkamp space of a combinatorial Grassmannian of type G 2 ( 7 ) , V ( G 2 ( 7 ) ) . The lines of the ambient symplectic polar space are those lines of V ( G 2 ( 7 ) ) whose cores feature an odd number of points of G 2 ( 7 ) . After introducing the basic properties of three different types of points and seven distinct types of lines of V ( G 2 ( 7 ) ) , we explicitly show the combinatorial Grassmannian composition of the magic Veldkamp line; we first give representatives of points and lines of its core generalized quadrangle GQ ( 2 , 2 ) , and then additional points and lines of a specific elliptic quadric Q - (5, 2), a hyperbolic quadric Q + (5, 2), and a quadratic cone Q ^ (4, 2) that are centered on the GQ ( 2 , 2 ) . In particular, each point of Q + (5, 2) is represented by a Pasch configuration and its complementary line, the (Schläfli) double-six of points in Q - (5, 2) comprise six Cayley–Salmon configurations and six Desargues configurations with their complementary points, and the remaining Cayley–Salmon configuration stands for the vertex of Q ^ (4, 2). Full article
(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Modeling the process of differentiation with open quantum systems
Author: Masanari Asano, Tokuyama College of Technology, Japan; E-Mail: asano@tokuyama.ac.jp

Title: Decision making from stabilization of oscillations of a systems interacting with information environment
Author: Fabio Bagarello, Palermo University, Italy; E-Mail: fabio.bagarello@unipa.it

Title: Decision making as decoherence
Author: Irina Basieva, City University of London, UK; E-Mail: Irina.Basieva@gmail.com

Title: TBA
Author: Giacomo Mauro D'Ariano, University of Pavia, Italy; E-Mail: dariano@unipv.it

Title: Contextuality and Causality
Author: Ehtibar Dzhafarov, Purdue University, USA; E-Mail: ehtibar@purdue.edu

Title: Transition from possible to actual and the Gibbs ensemble
Author: Gregg Jaeger, Boston University, USA; E-Mail: gsjaeger@gmail.com

Title: Quantum information modeling of cognition
Author: Andrei Khrennikov, Linnaeus University, Sweden; E-Mail: Andrei.Khrennikov@lnu.se

Title: Some Quantum Concepts in Information Access and Retrieval
Author: Massimo Melucci, University of Padova, Italy; E-Mail: melo@dei.unipd.it

Title: TBA
Author: Adan Cabello, Universidad de Sevilla, Spain; E-Mail: adan@us.es

Title: Resistance to noise of a nonlocal N-qudit state for N>=3
Author: Elena Loubenets, National Research University Higher School of Economics, Russia; E-Mail:

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