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prospects of proposals such as quantum-interferometric optical lithography. The method can be adapted to generate entangled states of arbitrarily large photon number. Because prior entanglement is not required, the procedure would work well with singlephoton-on-demand sources 29,30 , which promise to be more efficient and scalable than down-conversion sources. Scalability would also be enhanced by the use of photon-number-resolving detectors. The construction proceeds from spatially separated, unentangled photons to a maximally entangled state in a single spatial mode, a state suitable for Heisenberg-limited phase measurements.A

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