View source for 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
{{Equation|<math>H = H_S\otimes I_B + I_S\otimes H_B + H_I, \,\!</math>|10.1}}
where <math>H_S \,\!</math> acts only on the system, <math>H_B\,\!</math> acts only on the bath, and 
{{Equation|<math> H_I = \sum_\alpha S_\alpha\otimes B_\alpha, \,\!</math>|10.2}}
is the interaction Hamiltonian with the <math>S_\alpha\,\!</math> acting only on the system and the <math>B_\alpha\,\!</math> acting only on the bath.