Superselection Rules, Quantum Error Correction, and Quantum Chromodynamics

TL;DR

This paper explores how superselection rules relate to quantum error correction, showing that superselection rules imply error correction conditions and analyzing quantum chromodynamics as a case study for protected quantum information.

Contribution

It establishes a link between superselection rules and quantum error correction, and applies this framework to quantum chromodynamics and topological codes.

Findings

Superselection rules imply the Knill-Laflamme condition.

Quantum chromodynamics states can serve as superselection sectors protecting information.

Discussion of topological codes and supersymmetric quantum field theory within this context.

Abstract

We investigate the relationship between superselection rules and quantum error correcting codes. We demonstrate that the existence of a superselection rule implies the Knill-Laflamme condition in quantum error correction. As an example, we examine quantum chromodynamics through the lens of quantum error correction, where the proton and neutron states in the model are explored as different superselection sectors that protect logical information. Finally we comment on topological quantum error correcting codes and supersymmetric quantum field theory within this framework.