Linear optical fusion gate onto qubits boosted by high-dimensional entanglement

Photonic modes are suitable to carry high-dimensional quantum information as qudits, and the use of high-dimensional entanglement between qudits is expected to increase the information capacity. However, compared with the use of photonic modes as qubits, it is much more difficult to process qudits with keeping their dimensions, e.g., to generate multi-partite entangled qudits with linear optics, which considerably narrows the range of applications as qudits. We propose linear optical fusion gates which project a pair of qudit systems onto a Bell state in two-dimensional subspaces. These enable us to generate a two-dimensional Bell state by applying it to halves of two pairs of d-dimensional maximally entangled states with success probability 1-1/d without ancilla photons (1-1/d^l+1 with 2(2^l-1) ancilla photons (l=1, 2, ...)). These success probabilities are higher than the conventional type-II fusion gates, corresponding to d=2. Thus, this work increases usability of photonic qudits, especially in efficient generation of large-scale multipartite two-dimensional entangled states for quantum computation and communication.