Generalizations of Pauli channels

TL;DR

This paper generalizes Pauli channels to n-level quantum systems by constructing trace-preserving maps that act as depolarizing channels on complementary subalgebras, providing conditions for complete positivity.

Contribution

It introduces a framework for generalized Pauli channels on higher-dimensional systems using complementary subalgebras, with a complete positivity criterion.

Findings

Characterization of complete positivity conditions

Construction of depolarizing channels on subalgebras

Applications to bipartite quantum systems

Abstract

The Pauli channel acting on 2 x 2 matrices is generalized to an n-level quantum system. When the full matrix algebra M is decomposed into pairwise complementary subalgebras, then trace-preserving linear mappings from M to M are constructed such that the restriction to the subalgebras are depolarizing channels. The result is the necessary and sufficient condition of complete positivity. The main examples appear on bipartite systems