  We propose a single-photon-by-single-photon all-optical switch concept based
on interference-localized states on lattices and their delocalization by
interaction. In its 'open' operation, the switch stops single photons while
allows photon pairs to pass the switch. Alternatively, in the 'closed'
operation, the switch geometrically separates single-photon and two-photon
states. We demonstrate the concept using a three-site Stub unit cell and the
diamond chain. The systems are modeled by Bose-Hubbard Hamiltonians, and the
dynamics is solved by exact diagonalization with Lindblad master equation. We
discuss realization of the switch using photonic lattices with nonlinearities,
superconductive qubit arrays, and ultracold atoms. We show that the switch
allows arbitrary 'ON'/'OFF' contrast while achieving picosecond switching time
at the single-photon switching energy with contemporary photonic materials.
