Figure 1

Generation of multipartite entangled or cluster states by the use of SLM. The overall output from SPDC is divided in spatial sections, and a different phase may be imposed to each portion in a programmable way, corresponding to the application of controlled phase gates. Each spatial section includes several pixels. In (b) we report the momentum state in our experimental implementation $|\Psi \rangle =\frac{1}{\sqrt{2}}|0\rangle {}_i(|0\rangle {}_s+|1\rangle {}_s)$; in (c) the state configuration to achieve $|\Psi \rangle =\frac{1}{2}(|0\rangle {}_i+|1\rangle {}_i)(|0\rangle {}_s+|1\rangle {}_s)$ (which may become $|\Psi \rangle =\frac{1}{\sqrt{2}}(|0\rangle |1\rangle +|1\rangle |0\rangle )$ upon the use of a spectral filter, bandpass of 10 nm). In (d) the generic configuration leads to the momentum state $|\Psi \rangle =|s\rangle \otimes |i\rangle$.Reuse & Permissions

Figure 2

Experimental setup. Polarization entangled states are generated by down-conversion in type-I BBO crystals pumped at 405 nm by a Newport LQC 405-40P cw laser diode. Then, a spatial section of the output cones passes through the SLM which (at the same time) i) provides purification of polarization entanglement and ii) introduces a position- (i.e., generation angle) dependent phase shift between the two polarizations. After SLM, there are (on both paths) a slit, an iris, two long-pass filters (cut-on wavelength $=$ 715 nm), a coupler with an $1/e^2$ output beam diameter of 7.14 mm, and a multimode optical fiber that directs the photons to the detector. The detectors are homemade single-photon counting modules ($D1,D2$), based on an avalanche photodiode operated in Geiger mode with passive quenching. For tomographic reconstruction we insert a quarter-wave plate, a half-wave plate, and a polarizer and for the optimization of the phase functions only the polarizers.Reuse & Permissions

Figure 3

Coincidence counts on a time window of 30 s with the polarizers in front of the couplers set at ${45}^{°}$ and $-{45}^{°}$. (a) Coincidences as a function of $b_1$ (blue) and $b_2$ (red) with $b_{2,1}=0$ and optimal $a_{1,2}$; (b) coincidences as a function of $a_1=-a_2$ with optimal $b_1$ and $b_2=0$.Reuse & Permissions

Figure 4

Characterization of the output state. In (a) we report the tomographic reconstruction (real part) of the global purified polarization entangled state prior to the action of the phase gate, whereas in (b) we show the corresponding visibility curve and the fit with the curve $\cos {}^2({\alpha }_2-{45}^{°})$ (solid line). In (c) and (d) we report the tomographic reconstructions (real part) of the reduced states ${\varrho }_0$ and ${\varrho }_1$.Reuse & Permissions