  We analyze decoherence-free (DF) quantum information in the presence of an
arbitrary non-nearest-neighbor bath-induced system Hamiltonian using a
Markovian master equation. We show that the most appropriate encoding for N
qubits is probably contained within the ~(2/9) N excitation subspace. We give a
timescale over which one would expect to apply other methods to correct for the
system Hamiltonian. In order to remain applicable to experiment, we then focus
on small systems, and present examples of DF quantum information for three and
four qubits. We give an encoding for four qubits that, while quantum
information remains in the two-excitation subspace, protects against an
arbitrary bath-induced system Hamiltonian. Although our results are general to
any system of qubits that satisfies our assumptions, throughout the paper we
use dipole-coupled qubits as an example physical system.
