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PHYSICS (573 journals)

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Journal Cover Reviews in Mathematical Physics
  [SJR: 1.092]   [H-I: 36]   [0 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0129-055X - ISSN (Online) 1793-6659
   Published by World Scientific Homepage  [118 journals]
  • Erratum: "Quantum [math]-divergences and error correction"
    • Authors: Fumio Hiai, Milán Mosonyi, Dénes Petz, Cédric Bény
      Abstract: Reviews in Mathematical Physics, Volume 29, Issue 07, August 2017.

      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-02T04:06:22Z
      DOI: 10.1142/S0129055X17920015
       
  • Derivation of the Hartree equation for compound Bose gases in the mean
           field limit
    • Authors: Ioannis Anapolitanos, Michael Hott, Dirk Hundertmark
      Abstract: Reviews in Mathematical Physics, Volume 29, Issue 07, August 2017.
      We consider mixtures of Bose gases of different species. We prove that in the mean field limit and under suitable conditions on the initial condition, a system composed of two Bose species can be effectively described by a system of coupled Hartree equations. Moreover, we derive quantitative bounds on the rates of convergence of the reduced density matrices in Sobolev trace norms. We treat both the non-relativistic case in the presence of an external magnetic field [math] and the semi-relativistic case.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-02T04:06:21Z
      DOI: 10.1142/S0129055X17500222
       
  • Different quantum [math]-divergences and the reversibility of quantum
           operations
    • Authors: Fumio Hiai, Milán Mosonyi
      Abstract: Reviews in Mathematical Physics, Volume 29, Issue 07, August 2017.
      The concept of classical [math]-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the Rényi divergences. Various quantum versions of this concept, and more narrowly, the concept of Rényi divergences, have been introduced in the literature with applications in quantum information theory; most notably Petz’ quasi-entropies (standard [math]-divergences), Matsumoto’s maximal [math]-divergences, measured [math]-divergences, and sandwiched and [math]-[math]-Rényi divergences. In this paper, we give a systematic overview of the various concepts of quantum [math]-divergences, with a main focus on their monotonicity under quantum operations, and the implications of the preservation of a quantum [math]-divergence by a quantum operation. In particular, we compare the standard and the maximal [math]-divergences regarding their ability to detect the reversibility of quantum operations. We also show that these two quantum [math]-divergences are strictly different for non-commuting operators unless [math] is a polynomial, and obtain some analogous partial results for the relation between the measured and the standard [math]-divergences. We also study the monotonicity of the [math]-[math]-Rényi divergences under the special class of bistochastic maps that leave one of the arguments of the Rényi divergence invariant, and determine domains of the parameters [math] where monotonicity holds, and where the preservation of the [math]-[math]-Rényi divergence implies the reversibility of the quantum operation.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-08-02T04:06:17Z
      DOI: 10.1142/S0129055X17500234
       
  • Remarks on BEC on graphs
    • Authors: Tomohiro Kanda
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We consider Bose–Einstein condensation (BEC) on graphs with transient adjacency matrix. We prove the equivalence of BEC and non-factoriality of the quasi-free state. Moreover, quasi-free states exhibiting BEC decompose into generalized coherent states. We review necessary and sufficient conditions that a quasi-free state is faithful, factor, and pure and quasi-free states are quasi-equivalent, including the papers of Araki and Shiraishi [1], Araki [2], and Araki and Yamagami [3]. Using their formats and results, we prove necessary and sufficient conditions that a generalized coherent state is faithful, factor, and pure and generalized coherent states are quasi-equivalent as well.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-07-19T06:48:10Z
      DOI: 10.1142/S0129055X17500246
       
  • Covariant KSGNS construction and quantum instruments
    • Authors: Erkka Haapasalo, Juha-Pekka Pellonpää
      Abstract: Reviews in Mathematical Physics, Ahead of Print.
      We study completely positive (CP) [math]-sesquilinear-form-valued maps on a unital [math]-algebra [math], where the sesquilinear forms operate on a module over a [math]-algebra [math]. We also study the cases when either one or both of the algebras are von Neumann algebras. Moreover, we assume that the CP maps are covariant with respect to actions of a symmetry group. This allows us to view these maps as generalizations of covariant quantum instruments. We determine minimal covariant dilations (KSGNS constructions) for covariant CP maps to find necessary and sufficient conditions for a CP map to be extreme in convex subsets of normalized covariant CP maps. As a special case, we study covariant quantum observables and instruments whose value space is a transitive space of a unimodular type-I group. Finally, we discuss the case of instruments that are covariant with respect to a square-integrable representation.
      Citation: Reviews in Mathematical Physics
      PubDate: 2017-06-13T09:19:49Z
      DOI: 10.1142/S0129055X17500209
       
 
 
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