Fundamental Limits on N-photon Absorption Rate for N Spatially Entangled Photons

It is shown, via a rigorous formalism and specific examples, that the N-photon absorption rate is fundamentally reduced when N entangled photons are used to reduce the spatial feature size of the absorption pattern. This result contradicts the heuristic argument in the original proposal of quantum lithography [Boto et al., Phys. Rev. Lett. 85, 2733 (2000)]. Furthermore, the quantum enhancement of the multiphoton absorption rate, if spatial resolution of the exposure is forgone, is shown to asymptotically approach a fixed value for large N, unlike other types of quantum-enhanced measurements. This enhancement due to spatial entanglement is potentially useful for multiphoton spectroscopy, where spatial resolution is not needed