The structure of preserved information in quantum processes

TL;DR

This paper provides a unified framework for understanding information-preserving structures in quantum processes, showing they are isometric to fixed points and form matrix algebras, with practical algorithms for identifying noiseless subsystems.

Contribution

It introduces a general operational characterization of IPS, unifies various concepts, and offers an efficient method to find noiseless subsystems in quantum processes.

Findings

IPS are isometric to fixed points of unital quantum processes.

Every IPS forms a matrix algebra.

Provides an algorithm to identify noiseless subsystems.

Abstract

We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every IPS is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrodinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process.