  We analyze the problem of increasing the efficiency of single-photon sources
or single-rail photonic qubits via linear optical processing and destructive
conditional measurements. In contrast to previous work we allow for the use of
coherent states and do not limit to photon-counting measurements. We conjecture
that it is not possible to increase the efficiency, prove this conjecture for
several important special cases, and provide extensive numerical results for
the general case.
