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 performed using linear-optical circuits with the success probabilities of 1-d⁻¹ without ancilla photons and 1-d⁻⁽ᵏ⁺¹⁾ with 2(2ᵏ-1) ancilla photons. It allows us to entangle two independently-prepared high-dimensional entangled states two-dimensionally with higher 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.