Figure 3

Closed-loop set-up.

(a) Conceptual scheme. Qubits A and B are prepared in the Bell state |Ψ⁻〉, the environment O, initially in the state |0〉, undergoes a rotation R_O(p) that splits its state between the “up” and “down” paths. O then interacts with qubit B through a controlled-NOT gate (CNOT). O is measured in a rotated basis by which gives a result k (either the “θ_u” or the “θ_d” path). The environment interaction can be corrected with a unitary . E_f: entanglement of formation measurement. (b) Experimental implementation. “u” and “d”: “up” and “down” path states of the environment, BS: balanced beam-splitter, AF: attenuation filter, φ: thin glass plate to adjust the phase φ = 2θ, HWP: half-wave plate, QWP: quarter-wave plate, PBS: polarizing beam-splitter, SPAD: single photon avalanche photodiode, C: coincidence counting electronics. (c) Actual experimental set-up for photon B, see Methods. The red paths correspond to the “O-B interaction” part, the pink to the “O measurement” and the blue to the “controlled correction” and polarization tomographic measurement. Both exit modes “θ_u” and “θ_d” of (b) are measured successively on the same exit port “θ_u/d” for two complementary phase settings φ and π − φ; the control HWP at 45° is inserted only for π − φ.