On k-decomposability of positive maps

TL;DR

This paper advances the understanding of positive maps in quantum theory by characterizing k-positive maps and exploring their relation to modular theory, thereby extending the theory of decomposable maps.

Contribution

It provides a detailed description of k-positive maps and links transposition with modular theory, enriching the structural understanding of positive maps.

Findings

Characterization of k-positive maps

Relation established between transposition and modular theory

Analysis of positive maps via generalized Tomita-Takesaki scheme

Abstract

We extend the theory of decomposable maps by giving a detailed description of k-positive maps. A relation between transposition and modular theory is established. The structure of positive maps in terms of modular theory (the generalized Tomita-Takesaki scheme) is examined.