  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 $2(2^{k}-1)$ 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.
