Linear-Optical Fusion Boosted by High-Dimensional Entanglement

We propose a quantum measurement that probabilistically projects a pair of qudits of dimension d onto a Bell state in a two-qubit subspace. It can be implemented using linear-optical circuits with the success probabilities of 1-d^{-1} without ancilla photons and 1-d^{-(k+1)} with 2(2^{k}-1) ancilla photons. It allows us to entangle two independently prepared high-dimensional entangled states two dimensionally with higher success probabilities than ones of linear-optical fusion gates on qubits. As an application, we propose a fast quantum repeater protocol with three-qudit GHZ states and quantum memories.