Pauli component erasing quantum channels

TL;DR

This paper introduces Pauli component erasing quantum channels that selectively preserve or erase parts of multi-qubit systems, providing a complete characterization, understanding their structure, and linking them to Markovian processes.

Contribution

It defines and characterizes a new family of quantum channels that selectively erase or preserve Pauli components in multi-qubit systems, including their algebraic structure and physical implementation.

Findings

The channels form a semigroup with identifiable generators.

Preserved components form a finite vector subspace.

Connections to Markovian processes are established.

Abstract

Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multi-qubit system in the basis of Pauli strings, which we call Pauli component erasing maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels forms a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.