Completely positive mappings and mean matrices

Ádám Besenyei, D. Petz

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Some functions f: ℝ+→ ℝ+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping JDf-1:Mn→Mn on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of JD f-1 in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.

Original languageEnglish
Pages (from-to)984-997
Number of pages14
JournalLinear Algebra and Its Applications
Volume435
Issue number5
DOIs
Publication statusPublished - Sep 1 2011

Fingerprint

Quantum Information
Positive definite matrix
Positivity
Monotonicity
Monotone
Concretes
Metric

Keywords

  • Completely positive mapping
  • Hadamard product
  • Logarithmic mean
  • Matrix means
  • Matrix monotone function

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis

Cite this

Completely positive mappings and mean matrices. / Besenyei, Ádám; Petz, D.

In: Linear Algebra and Its Applications, Vol. 435, No. 5, 01.09.2011, p. 984-997.

Research output: Contribution to journalArticle

Besenyei, Ádám ; Petz, D. / Completely positive mappings and mean matrices. In: Linear Algebra and Its Applications. 2011 ; Vol. 435, No. 5. pp. 984-997.
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