Figure 1

Experimental setup. Single 810 nm heralded photons are generated at a BBO crystal by type II parametric down conversion. Arbitrary states are prepared and measured with a combination of single qubit unitary gates and a controlled operation as exemplified in the inset, colors show the correspondence between circuit and physical implementation. Path-qubit unitary gates are controlled with phase plates and Sagnac interferometers. Polarization-qubit unitary gates are achieved with a combination of wave plates affecting both paths. A controlled operation with control on path and target in polarization is implemented with wave plates at different angles in each path. The different processes studied were set up in the zone marked as $\mathcal{E}$. Single-mode fibers clean the photon’s spatial mode ensuring good interferometer visibility ($>95\%$ in the Sagnacs and $\approx 90\%$ in the Mach-Zehnder). Not shown in the figure is the Mach-Zehnder’s active phase-sensitive stabilization mechanism (see supplemental material [17]).Reuse & Permissions

Figure 2

Full reconstruction of two channels. The $\chi$ matrices for (a) the identity process and (b) a controlled $U_c$ process (see text). Shown are the real and imaginary parts of each one all in excellent agreement with the expected theoretical results. The fidelity between these reconstructed processes and the ones reconstructed by the standard inefficient Nielsen and Chuang method are 91% and 93%, respectively.Reuse & Permissions

Figure 3

Efficient parameter estimation. By determining only some parameters characterizing a quantum channel different relevant questions can be answered. These parameters can be determined exactly or approximated by sampling over only some of the possible measurements needed to fully determine them. Depending on the complexity of the question more or less measurements are needed. In any case these values can be determined statistically with an error scaling with the amount of measurements better than $1/\sqrt{M}$ eliminating the need for exponential amount of measurements. Shown are the fidelities of the measured processes to two different target processes: the identity (left) and a controlled gate $U_c$ (right) as a function of the amount of measurements done and for ten different choice of sampling order. Results for different channels show how quickly the estimation can differentiate between each one and converge to a value close to the exact one. Also shown in black and colored dashed curves is the statistical maximum deviation expected for each result.Reuse & Permissions