Figure 2
From: Hyper-parallel nonlocal CNOT operation with hyperentanglement assisted by cross-Kerr nonlinearity
Quantum circuit for nonlocal implementation of CNOT operation in polarization DOF. Polarization Beam Splitter(PBS) transmit horizontal polarization and reflect vertical polarization. θ and −θ denote the cross-Kerr nonlinearities between the signal photons and the probe coherent beams. \({a}_{1},{b}_{1}\) are two spatial modes of photon \({A}_{1}\), \({a}_{2},{b}_{2},{a^{\prime} }_{2},{b^{\prime} }_{2}\) represent four spatial modes of photon \({A}_{2}\), \({a}_{3},{b}_{3}\) are two spatial modes of photon \({B}_{2}\), \({a}_{4},{b}_{4},{a^{\prime} }_{4},{b^{\prime} }_{4}\) represent four spatial modes of photon \({B}_{1}\). Beam Splitter (BS) can implement Hadamard operation in spatial-mode DOF. The wave plate \({R}_{45}\) is used to implement Hadamard operation in polarization DOF.
