An application of decomposable maps in proving multiplicativity of low dimensional maps

TL;DR

This paper introduces a class of maps demonstrating the multiplicativity of the maximal output p-norm for specific p values, expanding understanding of low-dimensional quantum maps.

Contribution

It identifies a new class of positive trace-preserving maps for which multiplicativity holds at p=2 and p≥4, advancing quantum information theory.

Findings

Multiplicativity holds for p=2 and p≥4 in the introduced class.

Includes all positive trace-preserving maps from 3D to 2D matrix algebras.

Provides new insights into low-dimensional quantum map properties.

Abstract

In this paper we present a class of maps for which the multiplicativity of the maximal output p-norm holds when p is 2 and p is larger than or equal to 4. The class includes all positive trace-preserving maps from the matrix algebra on the three-dimensional space to that on the two-dimensional.