Completely positive mappings and mean matrices
Adam Besenyei, Denes Petz
TL;DR
This paper investigates the complete positivity of linear mappings derived from functions that induce means of positive numbers and matrices, with applications in quantum information theory.
Contribution
It analyzes the complete positivity of these mappings for specific functions, advancing understanding in quantum information applications.
Findings
Identifies conditions under which the mappings are completely positive
Provides examples of functions f with positive definite matrix mappings
Connects mathematical properties to quantum information applications
Abstract
Some real functions f 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 linear mapping beta on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of beta in the case of a few concrete functions f. This problem has been motivated by applications in quantum information.
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Taxonomy
TopicsMathematical Inequalities and Applications · Matrix Theory and Algorithms · Functional Equations Stability Results