The Structure of Decoherence-free Subsystems

TL;DR

This paper develops a structural theory for decoherence-free subsystems in quantum information, providing algorithms for their maximal construction and applications in quantum many-body systems.

Contribution

It introduces a new structure theory for decoherence-free subsystems and an algorithm to identify maximal subsystems, with applications in quantum state analysis.

Findings

Algorithm for constructing maximal decoherence-free subsystems

Method to determine if two irreducible tensors are repeated

Application to quantum many-body state equivalence

Abstract

Decoherence-free subsystems have been successfully developed as a tool to preserve fragile quantum information against noises. In this letter, we develop a structure theory for decoherence-free subsystems. Based on it, we present an effective algorithm to construct a set of maximal decoherence-free subsystems in the sense that any other such subsystem is a subspace of one of them. As an application of these techniques in quantum many body systems, we propose a simple and numerically robust method to determine if two irreducible tensors are repeated, a key step in deciding if they are equivalent in generating matrix product states.