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Quantum Reports
Special Issues
Applications of Information Entropies in Quantum Science
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Applications of Information Entropies in Quantum Science

A special issue of Quantum Reports (ISSN 2624-960X).

Deadline for manuscript submissions: closed (31 July 2021) | Viewed by 12823

Special Issue Editor

Prof. Dr. Robin P. Sagar

E-Mail Website
Guest Editor
Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Ciudad de México 09340, Mexico
Interests: information theory in quantum chemistry; phase space distributions and continuous variable quantum information theory; entropic uncertainty relations; confined quantum systems

Special Issue Information

Dear Colleagues,

Information entropies, discrete or continuous, have been applied to examine the behavior and to quantify the uncertainty in underlying quantum distributions. The key here is the use of uncertainty as a conceptual tool for understanding quantum behavior. It did not escape attention that the Heisenberg uncertainty relation could be formulated in entropic terms, where the sum of the entropies in position and in momentum space is the information carrier. These applications, initiated in the study of atomic and molecular systems, have since migrated to encompass confined quantum systems, quantification of correlations, complexity studies, Bose–Einstein condensates, open quantum systems, design of functionals in density functional theory, and the theory of gravity as emergent phenomena. The discussion that was initiated with Shannon entropies has now been generalized to consider other uncertainty measures. Going forward, one would expect an increasing interaction between the quantum and other communities, to understand and to quantify quantum uncertainties.

The aim of this Special Issue is to catalogue the work that is being done in the application of information entropies to understand all aspects of quantum behavior.

Prof. Dr. Robin P. Sagar
Guest Editor

Manuscript Submission Information

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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. Quantum Reports is an international peer-reviewed open access quarterly 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 1400 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

  • Information entropies
  • Quantum uncertainties
  • Uncertainty measures
  • Correlation measures

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Published Papers (4 papers)

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Research

19 pages, 415 KiB  
Article
Shannon Entropy in Confined He-Like Ions within a Density Functional Formalism
by Sangita Majumdar and Amlan K. Roy
Quantum Rep. 2020, 2(1), 189-207; https://doi.org/10.3390/quantum2010012 - 10 Feb 2020
Cited by 25 | Viewed by 3228
Abstract
Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of [...] Read more.
Shannon entropy in position ( S r ) and momentum ( S p ) spaces, along with their sum ( S t ) are presented for unit-normalized densities of He, Li + and Be 2 + ions, spatially confined at the center of an impenetrable spherical enclosure defined by a radius r c . Both ground, as well as some selected low-lying singly excited states, viz., 1sns (n = 2–4) 3S, 1snp (n = 2–3) 3P, 1s3d 3D, are considered within a density functional methodology that makes use of a work function-based exchange potential along with two correlation potentials (local Wigner-type parametrized functional, as well as the more involved non-linear gradient- and Laplacian-dependent Lee-Yang-Parr functional). The radial Kohn-Sham (KS) equation is solved using an optimal spatial discretization scheme via the generalized pseudospectral (GPS) method. A detailed systematic analysis of the confined system (relative to the corresponding free system) is performed for these quantities with respect to r c in tabular and graphical forms, with and without electron correlation. Due to compression, the pattern of entropy in the aforementioned states becomes characterized by various crossovers at intermediate and lower r c regions. The impact of electron correlation is more pronounced in the weaker confinement limit and appears to decay with the rise in confinement strength. The exchange-only results are quite good to provide a decent qualitative discussion. The lower bounds provided by the entropic uncertainty relation hold well in all cases. Several other new interesting features are observed. Full article
(This article belongs to the Special Issue Applications of Information Entropies in Quantum Science)
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7 pages, 293 KiB  
Article
Information Entropy Approach for a Disorderless One-Dimensional Lattice
by Luis Arturo Juárez-Villegas and Moisés Martínez-Mares
Quantum Rep. 2020, 2(1), 107-113; https://doi.org/10.3390/quantum2010008 - 29 Jan 2020
Cited by 3 | Viewed by 2130
Abstract
Dimensionless conductance through a disorderless lattice is studied using an alternative approach. Usually, the conductance of an ordered lattice is studied at a fixed size, either finite or infinite if the crystalline limit is reached. Here, we propose one to consider the set [...] Read more.
Dimensionless conductance through a disorderless lattice is studied using an alternative approach. Usually, the conductance of an ordered lattice is studied at a fixed size, either finite or infinite if the crystalline limit is reached. Here, we propose one to consider the set of systems of all sizes from zero to infinite. As a consequence, we find that the conductance presents fluctuations, with respect to system size, at a fixed energy. At the band edge, these fluctuations are described by a statistical distribution satisfied by an ensemble of chaotic cavities with reflection symmetry, which also satisfies a maximum-entropy, or minimum-information, criterion. Full article
(This article belongs to the Special Issue Applications of Information Entropies in Quantum Science)
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13 pages, 495 KiB  
Article
Fidelity and Entropy Production in Quench Dynamics of Interacting Bosons in an Optical Lattice
by Rhombik Roy, Camille Lévêque, Axel U. J. Lode, Arnaldo Gammal and Barnali Chakrabarti
Quantum Rep. 2019, 1(2), 304-316; https://doi.org/10.3390/quantum1020028 - 15 Dec 2019
Cited by 10 | Viewed by 3192
Abstract
We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the [...] Read more.
We investigate the dynamics of a few bosons in an optical lattice induced by a quantum quench of a parameter of the many-body Hamiltonian. The evolution of the many-body wave function is obtained by solving the time-dependent many-body Schrödinger equation numerically, using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). We report the time evolution of three key quantities, namely, the occupations of the natural orbitals, that is, the eigenvalues of the one-body reduced density matrix, the many-body Shannon information entropy, and the quantum fidelity for a wide range of interactions. Our key motivation is to characterize relaxation processes where various observables of an isolated and interacting quantum many-body system dynamically converge to equilibrium values via the quantum fidelity and via the production of many-body entropy. The interaction, as a parameter, can induce a phase transition in the ground state of the system from a superfluid (SF) state to a Mott-insulator (MI) state. We show that, for a quench to a weak interaction, the fidelity remains close to unity and the entropy exhibits oscillations. Whereas for a quench to strong interactions (SF to MI transition), the relaxation process is characterized by the first collapse of the quantum fidelity and entropy saturation to an equilibrium value. The dip and the non-analytic nature of quantum fidelity is a hallmark of dynamical quantum phase transitions. We quantify the characteristic time at which the quantum fidelity collapses and the entropy saturates. Full article
(This article belongs to the Special Issue Applications of Information Entropies in Quantum Science)
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11 pages, 348 KiB  
Article
Shannon Entropy for the Hydrogen Atom Confined by Four Different Potentials
by Michael-Adán Martínez-Sánchez, Rubicelia Vargas and Jorge Garza
Quantum Rep. 2019, 1(2), 208-218; https://doi.org/10.3390/quantum1020018 - 1 Nov 2019
Cited by 28 | Viewed by 3635
Abstract
Spatial confinements induce localization or delocalization on the electron density in atoms and molecules, and the hydrogen atom is not the exception to these results. In previous works, this system has been confined by an infinite and a finite potential where the wave-function [...] Read more.
Spatial confinements induce localization or delocalization on the electron density in atoms and molecules, and the hydrogen atom is not the exception to these results. In previous works, this system has been confined by an infinite and a finite potential where the wave-function exhibits an exact solution, and, consequently, their Shannon entropies deliver exact results. In this article, the Shannon entropy in configuration space is examined for the hydrogen atom submitted to four different potentials: (a) infinite potential; (b) Coulomb plus harmonic oscillator; (c) constant potential; and (d) dielectric continuum. For all these potentials, the Schrödinger equation admitted an exact analytic solution, and therefore the corresponding electron density has a closed-form. From the study of these confinements, we observed that the Shannon entropy in configuration space is a good indicator of localization and delocalization of the electron density for ground and excited states of the hydrogen atom confined under these circumstances. In particular, the confinement imposed by a parabolic potential induced characteristics that were not presented for other confinements; for example, the kinetic energy exhibited oscillations when the confinement radius is varied and such oscillations coincided with oscillations showed by the Shannon entropy in configuration space. This result indicates that, when the kinetic energy is increased, the Shannon entropy is decreased and vice versa. Full article
(This article belongs to the Special Issue Applications of Information Entropies in Quantum Science)
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