We expand the traditional two-photon Hong-Ou-Mandel (HOM) effect onto a higher-dimensional set of spatial modes. This enables a quantum network router that provides a controllable redistribution of entangled photon states over four spatial modes using a novel idea of directionally unbiased linear-optical Grover four-ports. The familiar Hong-Ou-Mandel (HOM) effect occurs when two indistinguishable photons impinge on adjacent ports of a 50:50 beam-splitter. Two-photon interference causes the photons to always emerge from the same output port in the same spatial mode. This traditional HOM method, observed on a beam-splitter with two input and two output ports, always has the two-photon state simultaneously occupying both output spatial modes, leaving no room to alter the propagation direction of outgoing states. The presented higher-dimensional HOM effect allows manipulation of quantum photon amplitudes in four spatial modes by using directionally unbiased linear-optical devices such as Grover coin optical multiports, beam splitters, and phase shifters. This could be used as a linear-optical switch /router for quantum networks.
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