An Approach by Representation of Algebras for Decoherence-Free Subspaces

TL;DR

This paper introduces an algebraic framework for Decoherence-Free Subspaces in quantum systems, utilizing semisimple algebras, Clifford algebras, and group theory to enhance understanding and applications in quantum decoherence mitigation.

Contribution

It generalizes algebraic results for DFSs, integrating Clifford algebras and minimal ideals, and connects quantum chemistry applications with this formalism.

Findings

Derived orthogonality theorems for algebraic structures

Built DFSs using tensor products of Clifford algebras

Linked algebraic formalism to quantum chemistry applications

Abstract

The aim of this paper is to present a general algebraic formulation for the Decoherence-Free Subspaces (DFSs). For this purpose, we initially generalize some results of Pauli and Artin about semisimple algebras. Then we derive orthogonality theorems for algebras analogous to finite groups. In order to build the DFSs we consider the tensor product of Clifford algebras and left minimal ideals. Furthermore, we show that standard applications of group theory in quantum chemistry can be obtained in our formalism. Advantages and some perspectives are also discussed.