Chapter 10 - Decoherence-Free/Noiseless Subsystems

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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


(10.1)

where acts only on the system, acts only on the bath, and


(10.2)

is the interaction Hamiltonian with the acting only on the system and the acting only on the bath.