Special Issue "Mathematical Physics and Quantum Information"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (31 January 2019)

Special Issue Editor

Guest Editor
Prof. Michel Planat

Institut FEMTO-ST, 15B Avenue des Montboucons, 25000 Besançon, France
Website | E-Mail
Interests: Physics: quantum computing, quantum information, signal processing, mathematical physics; Mathematics: group theory, knot theory, discrete mathematics, graph theory, number theory, finite geomety

Special Issue Information

Dear Colleagues,

Wigner’s “unreasonable effectiveness of mathematics” applies to foundational problems in quantum information theory (QIT) and the puzzles of quantum mechanics (EPR, Kochen-Specker, Schr¨odinger’s cat). Advanced mathematical concepts such as finite simple groups and the related finite geometries, algebraic combinatorics, number theory, the modularity theorem and operator algebras have been shown to play a significant role in QIT. Finding efficient quantum codes and algorithms, modeling quantum communication channels, generalized quantum measurements (POVMs) and the representation of quantum computing are some instances of the usefulness of mathematics in quantum physics. Finally quantum-like cognition and the quantum mind are valid concepts pertaining to the boundary of mathematics and the human mind that needs further study.

The Guest Editor solicits papers dealing with these challenging questions in the language of mathematics.

Prof. Dr. Michel Planat
Guest Editor

Manuscript Submission Information

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Keywords

  • Quantum information theory (QIT)
  • Foundations of quantum mechanics
  • Quantum entanglement
  • Quantum contextuality
  • Quantum channels
  • Quantum codes
  • Quantum computing
  • Quantum cognition
  • Informationally complete POVMs
  • Phase space methods
  • Quantum probability
  • Group theory
  • Number theory
  • Operator algebras

Published Papers (1 paper)

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Research

Open AccessFeature PaperArticle
Acting Semicircular Elements Induced by Orthogonal Projections on Von-Neumann-Algebras
Mathematics 2017, 5(4), 74; https://doi.org/10.3390/math5040074
Received: 18 September 2017 / Revised: 20 November 2017 / Accepted: 21 November 2017 / Published: 6 December 2017
PDF Full-text (398 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, we construct a free semicircular family induced by Z-many mutually-orthogonal projections, and construct Banach ∗-probability spaces containing the family, called the free filterizations. By acting a free filterization on fixed von Neumann algebras, we construct the corresponding Banach ∗-probability [...] Read more.
In this paper, we construct a free semicircular family induced by Z -many mutually-orthogonal projections, and construct Banach ∗-probability spaces containing the family, called the free filterizations. By acting a free filterization on fixed von Neumann algebras, we construct the corresponding Banach ∗-probability spaces, called affiliated free filterizations. We study free-probabilistic properties on such new structures, determined by both semicircularity and free-distributional data on von Neumann algebras. In particular, we study how the freeness on free filterizations, and embedded freeness conditions on fixed von Neumann algebras affect free-distributional data on affiliated free filterizations. Full article
(This article belongs to the Special Issue Mathematical Physics and Quantum Information)
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