Chapter 10 - Decoherence-Free/Noiseless Subsystems

Introduction

In the last chapter we saw that it is possible, at least in principle, to detect and correct errors in quantum systems. Here a different method for protecting against errors is explored. This method encodes information into quantum states such that the information avoids errors. The information is encoded in such a way that it is invariant under the errors produced by the system-bath interaction Hamiltonian. The initial work involved what are called decoherence-free subspaces and was later generalized to subsystems. (This work is reviewed in Whaley/Lidar and Byrd/Wu/Lidar.)

In what follows, a general quantum system will be assumed to be coupled non-trivially to a bath such that the entire system-bath Hamiltonian is given by