Chapter 8 - 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 Hamiltonian. The initial work involved what are called decoherence-free subspaces and was later generalized to subsystems. (These terms are defined below. Reviews may be found 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

	$H=H_{S}\otimes I_{B}+I_{S}\otimes H_{B}+H_{I},\,\!$	(8.1)

where $H_{S}\,\!$ acts only on the system, $H_{B}\,\!$ acts only on the bath, and

	$H_{I}=\sum _{\alpha }S_{\alpha }\otimes B_{\alpha },\,\!$	(8.2)

is the interaction Hamiltonian with the $S_{\alpha }\,\!$ acting only on the system and the $B_{\alpha }\,\!$ acting only on the bath.