We theoretically investigate and experimentally demonstrate a procedure for conditional control and enhancement of an interferometric coupling between two qubits encoded into states of bosonic particles. Our procedure combines local coupling of one of the particles to an auxiliary mode and single-qubit quantum filtering. We experimentally verify the proposed procedure using a linear optical setup where qubits are encoded into quantum states of single photons and coupled at a beam splitter with a fixed transmittance. With our protocol, we implement a range of different effective transmittances, demonstrate both enhancement and reduction of the coupling strength, and observe dependence of two-photon bunching on the effective transmittance. To make our analysis complete, we also theoretically investigate a more general scheme where each particle is coupled to a separate auxiliary mode and show that this latter scheme enables to achieve higher implementation probability. We show that our approach can be extended also to other kinds of qubit-qubit interactions.
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