Figure 1

Schematic diagram of experimental setup. A linearly polarized cw laser diode at 405 nm pumps a couple of BBO crystals cut for type-I downconversion. The horizontal and vertical photon pairs are balanced by a half-wave plate set along the pump path, whereas an additional BBO crystal (TC) is placed on the pump path to compensate the temporal delay. Signal and idler beams travel through the SLM, which provides entanglement purification and imposes the space-dependent phase functions ${\phi }^{\left(s\right)}\left(\theta \right),{\phi }^{\left(i\right)}\left({\theta }^{\prime }\right)$, and then are spatially selected by two irises and two slits set at $D=500$ mm with $\Delta x=5$ mm ($\Delta =10$ mrad). An interference filter IF (FWHM 10 nm around the central wavelength 810 nm) set on the signal path selects the spectral width, while a long-pass filter LF, cut-on wavelength 715 nm, is set on the idler path in order to reduce the background. Photons are focused in two multimode fibers (MMFs) and sent to single-photon counting modules. Polarizers at the angles $\pi /4$ and $3\pi /4$ or $\pi /4$ and $\pi /4$ are inserted to measure visibility whereas a quarter-wave plate, a half-wave plate, and a polarizer (not shown in the figure) are used for the tomographic reconstruction.Reuse & Permissions

Figure 2

Effect of the interference filter to narrow the output spectral range and achieve spatial entanglement. The plot shows coincidence count distribution $C$ with $\Delta$ $=$ 1 mrad and polarizers at $P=P^{\prime }=H$ [see Eq. (7)], measured within a coincidence time window of 50 ns, as a function of the signal and idler slit positions $\theta$ and ${\theta }^{\prime }$. The phase-matching central angles correspond to ${\theta }_0,{\theta }_0^{\prime }=0$.Reuse & Permissions

Figure 3

Phase imaging after inserting the phase function ${\phi }^{\left(s\right)}\left(\theta \right)=a\sin \left(k\theta \right)$ on the signal beam, with $a=1.35$ rad and $k\simeq 0.57$ mrad${}^{-1}$. Blue squares are the direct counts whereas red circles are the coincidences. Solid lines are the corresponding theoretical predictions (blue and red lines, respectively) as a function of the idler slit position. From the coincidence counts observed by scanning the idler beam, one can reconstruct the phase function along the signal beam.Reuse & Permissions

Figure 4

Tomographic reconstruction (the real part of the density matrix on the left and the imaginary one on the right) of the state in which we insert ${\phi }^{\left(i\right)}={\phi }^{\left(s\right)}=a\sin \left(k\theta \right)$, with $a=1.35$ rad and $k\simeq 0.57$ mrad${}^{-1}$ (upper panels) and of the state obtained with ${\phi }^{\left(i\right)}=-{\phi }^{\left(s\right)}$ (lower panels). The corresponding visibilities are given by $0.888\pm 0.003$ and $0.057\pm 0.014$, while the measured CHSH-Bell parameters are $B=2.658\pm 0.011$ and $B=1.854\pm 0.012$, respectively.Reuse & Permissions

Figure 5

Quantum key distribution by nonlocal phase compensation. The four blocks of data in the plot are the coincidence counting rates in the four different configurations $[++/1]$, $[++/0]$, $[+-/1]$, and $[+-/0]$, respectively The first two configurations correspond to the faithful transmission of the key, whereas the two others cases are the events that Alice and Bob are going to reject in the sifting stage of the protocol.Reuse & Permissions