  We show how an idealised measurement procedure can condense photons from two
modes into one, and how, by feeding forward the results of the measurement, it
is possible to generate efficiently superpositions of components for which only
one mode is populated, commonly called ``N00N states''. For the basic
procedure, sources of number states leak onto a beam splitter, and the output
ports are monitored by photodetectors. We find that detecting a fixed fraction
of the input at one output port suffices to direct the remainder to the same
port with high probability, however large the initial state. When instead
photons are detected at both ports, Schr\"{o}dinger cat states are produced. We
describe a circuit for making the components of such a state orthogonal, and
another for subsequent conversion to a N00N state. Our approach scales
exponentially better than existing proposals. Important applications include
quantum imaging and metrology.
