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The multi-mode character of quantum fields imposes constraints on theimplementation of high-fidelity quantum gates between individual photons. Sofar this has only been studied for the longitudinal degree of freedom. Here weshow that effects due to the transverse degrees of freedom significantly affectquantum gate performance. We also discuss potential solutions, in particularseparating the two photons in the transverse direction.

Transverse multi-mode effects on the performance of photon-photon gates