  We introduce a generalized theory of decoherence-free subspaces and
subsystems (DFSs), which do not require accurate initialization. We derive a
new set of conditions for the existence of DFSs within this generalized
framework. By relaxing the initialization requirement we show that a DFS can
tolerate arbitrarily large preparation errors. This has potentially significant
implications for experiments involving DFSs, in particular for the experimental
implementation, over DFSs, of the large class of quantum algorithms which can
function with arbitrary input states.
