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Quantum Mechanics: From Foundations to Information Technologies

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

Deadline for manuscript submissions: closed (1 February 2018) | Viewed by 49577

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Special Issue Editors

Prof. Dr. Giacomo Mauro D'Ariano

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Guest Editor

QUit Group, Department of Physics, University of Pavia, I-27100 Pavia, Italy
Interests: quantum information; foundations of quantum physics; foundations of quantum field theory; tension between quantum theory and general relativity
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Andrei Khrennikov

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Guest Editor

International Center for Mathematical Modeling in Physics and Cognitive Sciences, Linnaeus University, SE-351 95 Växjö, Sweden
Interests: quantum foundations; information; probability; contextuality; applications of the mathematical formalism of quantum theory outside of physics: cognition, psychology, decision making, economics, finances, and 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
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Massimo Melucci

E-Mail Website
Guest Editor

Department of Information Engineering, University of Padua, 35131 Padova, Italy
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 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. 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 2600 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 (12 papers)

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14 pages, 437 KiB

Open AccessArticle

State Entropy and Differentiation Phenomenon

by Masanari Asano, Irina Basieva, Emmanuel M. Pothos and Andrei Khrennikov

Entropy 2018, 20(6), 394; https://0-doi-org.brum.beds.ac.uk/10.3390/e20060394 - 23 May 2018

Cited by 7 | Viewed by 3225

Abstract

In the formalism of quantum theory, a state of a system is represented by a density operator. Mathematically, a density operator can be decomposed into a weighted sum of (projection) operators representing an ensemble of pure states (a state distribution), but such decomposition is not unique. Various pure states distributions are mathematically described by the same density operator. These distributions are categorized into classical ones obtained from the Schatten decomposition and other, non-classical, ones. In this paper, we define the quantity called the state entropy. It can be considered as a generalization of the von Neumann entropy evaluating the diversity of states constituting a distribution. Further, we apply the state entropy to the analysis of non-classical states created at the intermediate stages in the process of quantum measurement. To do this, we employ the model of differentiation, where a system experiences step by step state transitions under the influence of environmental factors. This approach can be used for modeling various natural and mental phenomena: cell’s differentiation, evolution of biological populations, and decision making. Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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12 pages, 285 KiB

Open AccessArticle

Towards Experiments to Test Violation of the Original Bell Inequality

by Andrei Khrennikov and Irina Basieva

Entropy 2018, 20(4), 280; https://0-doi-org.brum.beds.ac.uk/10.3390/e20040280 - 13 Apr 2018

Cited by 10 | Viewed by 3889

Abstract

The aim of this paper is to attract the attention of experimenters to the original Bell (OB) inequality that was shadowed by the common consideration of the Clauser–Horne–Shimony–Holt (CHSH) inequality. There are two reasons to test the OB inequality and not the CHSH inequality. First of all, the OB inequality is a straightforward consequence to the Einstein–Podolsky–Rosen (EPR) argumentation. In addition, only this inequality is directly related to the EPR–Bohr debate. The second distinguishing feature of the OB inequality was emphasized by Itamar Pitowsky. He pointed out that the OB inequality provides a higher degree of violations of classicality than the CHSH inequality. For the CHSH inequality, the fraction of the quantum (Tsirelson) bound

Q_{CHSH} = 2 \sqrt{2}

to the classical bound

C_{CHSH} = 2,

i.e.,

F_{CHSH} = \frac{Q_{CHSH}}{C_{CHSH}} = \sqrt{2}

is less than the fraction of the quantum bound for the OB inequality

Q_{OB} = \frac{3}{2}

to the classical bound

C_{OB} = 1,

i.e.,

F_{OB} = \frac{Q_{OB}}{C_{OB}} = \frac{3}{2} .

Thus, by violating the OB inequality, it is possible to approach a higher degree of deviation from classicality. The main problem is that the OB inequality is derived under the assumption of perfect (anti-) correlations. However, the last few years have been characterized by the amazing development of quantum technologies. Nowadays, there exist sources producing, with very high probability, the pairs of photons in the singlet state. Moreover, the efficiency of photon detectors was improved tremendously. In any event, one can start by proceeding with the fair sampling assumption. Another possibility is to use the scheme of the Hensen et al. experiment for entangled electrons. Here, the detection efficiency is very high. Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

13 pages, 1390 KiB

Open AccessArticle

Contextuality Analysis of the Double Slit Experiment (with a Glimpse into Three Slits)

by Ehtibar N. Dzhafarov and Janne V. Kujala

Entropy 2018, 20(4), 278; https://0-doi-org.brum.beds.ac.uk/10.3390/e20040278 - 12 Apr 2018

Cited by 15 | Viewed by 4738

Abstract

The Contextuality-by-Default theory is illustrated on contextuality analysis of the idealized double-slit experiment. The experiment is described by a system of contextually labeled binary random variables each of which answers the question: Has the particle hit the detector, having passed through a given slit (left or right) in a given state (open or closed)? This system of random variables is a cyclic system of rank 4, formally the same as the system describing the Einsten-Podolsky-Rosen-Bell paradigm with signaling. Unlike the latter, however, the system describing the double-slit experiment is always noncontextual, i.e., the context-dependence in it is entirely explainable in terms of direct influences of contexts (closed-open arrangements of the slits) upon the marginal distributions of the random variables involved. The analysis presented is entirely within the framework of abstract classical probability theory (with contextually labeled random variables). The only physical constraint used in the analysis is that a particle cannot pass through a closed slit. The noncontextuality of the double-slit system does not generalize to systems describing experiments with more than two slits: in an abstract triple-slit system, almost any set of observable detection probabilities is compatible with both a contextual scenario and a noncontextual scenario of the particle passing though various combinations of open and closed slits (although the issue of physical realizability of these scenarios remains open). Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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17 pages, 1261 KiB

Open AccessArticle

Non-Hermitian Operator Modelling of Basic Cancer Cell Dynamics

by Fabio Bagarello and Francesco Gargano

Entropy 2018, 20(4), 270; https://0-doi-org.brum.beds.ac.uk/10.3390/e20040270 - 11 Apr 2018

Cited by 14 | Viewed by 2968

Abstract

We propose a dynamical system of tumor cells proliferation based on operatorial methods. The approach we propose is quantum-like: we use ladder and number operators to describe healthy and tumor cells birth and death, and the evolution is ruled by a non-hermitian Hamiltonian which includes, in a non reversible way, the basic biological mechanisms we consider for the system. We show that this approach is rather efficient in describing some processes of the cells. We further add some medical treatment, described by adding a suitable term in the Hamiltonian, which controls and limits the growth of tumor cells, and we propose an optimal approach to stop, and reverse, this growth. Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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13 pages, 259 KiB

Open AccessArticle

Quantifying Tolerance of a Nonlocal Multi-Qudit State to Any Local Noise

by Elena R. Loubenets

Entropy 2018, 20(4), 217; https://0-doi-org.brum.beds.ac.uk/10.3390/e20040217 - 23 Mar 2018

Viewed by 2898

Abstract

We present a general approach for quantifying tolerance of a nonlocal N-partite state to any local noise under different classes of quantum correlation scenarios with arbitrary numbers of settings and outcomes at each site. This allows us to derive new precise bounds in d and N on noise tolerances for: (i) an arbitrary nonlocal N-qudit state; (ii) the N-qudit Greenberger–Horne–Zeilinger (GHZ) state; (iii) the N-qubit W state and the N-qubit Dicke states, and to analyse asymptotics of these precise bounds for large N and

d .

Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

555 KiB

Open AccessArticle

The Poincaré Half-Plane for Informationally-Complete POVMs

by Michel Planat

Entropy 2018, 20(1), 16; https://0-doi-org.brum.beds.ac.uk/10.3390/e20010016 - 31 Dec 2017

Cited by 8 | Viewed by 4439

Abstract

It has been shown in previous papers that classes of (minimal asymmetric) informationally-complete positive operator valued measures (IC-POVMs) in dimension d can be built using the multiparticle Pauli group acting on appropriate fiducial states. The latter states may also be derived starting from [...] Read more.

H

. To do this, one translates the congruence (or non-congruence) subgroups of index d of the modular group into groups of permutation gates, some of the eigenstates of which are the sought fiducials. The structure of some IC-POVMs is found to be intimately related to the Kochen–Specker theorem. Full article

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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1220 KiB

Open AccessArticle

Quantum Minimum Distance Classifier

by Enrica Santucci

Entropy 2017, 19(12), 659; https://0-doi-org.brum.beds.ac.uk/10.3390/e19120659 - 01 Dec 2017

Cited by 6 | Viewed by 5005

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 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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260 KiB

Open AccessArticle

Coherent Processing of a Qubit Using One Squeezed State

by Allan Tameshtit

Entropy 2017, 19(12), 653; https://0-doi-org.brum.beds.ac.uk/10.3390/e19120653 - 30 Nov 2017

Cited by 3 | Viewed by 2577

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 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)

217 KiB

Open AccessArticle

“Wave-Packet Reduction” and the Quantum Character of the Actualization of Potentia

by Gregg Jaeger

Entropy 2017, 19(10), 513; https://0-doi-org.brum.beds.ac.uk/10.3390/e19100513 - 24 Sep 2017

Cited by 8 | Viewed by 4073

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 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)

3883 KiB

Open AccessArticle

Extraction of the Proton and Electron Radii from Characteristic Atomic Lines and Entropy Principles

by Edward Jiménez, Nicolás Recalde and Esteban Jiménez Chacón

Entropy 2017, 19(7), 293; https://0-doi-org.brum.beds.ac.uk/10.3390/e19070293 - 29 Jun 2017

Cited by 3 | Viewed by 6343

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 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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379 KiB

Open AccessArticle

A Functorial Construction of Quantum Subtheories

by Ivan Contreras and Ali Nabi Duman

Entropy 2017, 19(5), 220; https://0-doi-org.brum.beds.ac.uk/10.3390/e19050220 - 11 May 2017

Viewed by 4021

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.

(This article belongs to the Special Issue Quantum Mechanics: From Foundations to Information Technologies)

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Other

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235 KiB

Open AccessLetter

A Combinatorial Grassmannian Representation of the Magic Three-Qubit Veldkamp Line

by Metod Saniga

Entropy 2017, 19(10), 556; https://0-doi-org.brum.beds.ac.uk/10.3390/e19100556 - 19 Oct 2017

Cited by 2 | Viewed by 4341

Abstract

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 [...] 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

\hat{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