Figure 1

(a) Schematic of a generic quantum feedback control procedure. A “signal” qubit passes through a noisy channel, and is subsequently measured and corrected based on the result. Our scheme is shown schematically in the boxes. (b) Experimental diagram. Qubits are encoded in the polarization of single photons (horizontal $|H⟩\equiv |1⟩$, vertical $|V⟩\equiv |0⟩$) and manipulated with half wave plates (HWP) and quarter wave plates (QWP). Optical modes are overlapped on a partially polarizing beam splitter, with reflectivities $R_H=1/3$ ($R_V=1$) for horizontally (vertically) polarized light. Conditional on there being only one photon in each input and output mode, the gate ideally applies the operation $|0⟩⟨0|\otimes \mathbb{1}+|1⟩⟨1|\otimes Z$ [23, 24, 25]. The outcome of a projective measurement of the meter in the $+/-$ basis [19], using a polarizing beam splitter ($R_H=0$, $R_V=1$), determines a correction rotation on the signal qubit. Wave plate set $A$ corrects for unwanted polarization rotations induced by the fiber delay. A coincident detection event between either ($M_{+}$ and $S_1$) or ($M_{-}$ and $S_1$) signals a successful run. Photon pairs are generated via spontaneous parametric down-conversion (SPDC) of a type I BiBO crystal cut to produce degenerate 820 nm photon pairs. The crystal is pumped by a $\approx 100\mathrm{mW}$ beam at 410 nm produced from second harmonic generation of an 820 nm mode-locked Ti:sapphire laser (repetition rate 80 MHz). We spectrally filter the SPDC using $\pm 1\mathrm{nm}$ interference filters centered at 820 nm, then couple into two single mode fibers. Pump power is kept low to reduce the presence of multipair emission from SPDC [30, 31]. P CELL is a Pockels cell.Reuse & Permissions

Figure 2

(a) Contour plot of the optimal measurement strength $\cos {\chi }_{\mathrm{opt}}$ as a function of $p$ (the noise probability) and $\theta$ (half the angle between the two nonorthogonal qubit states, on the Bloch sphere). (b) Contour plot of ${\overline{F}}_{\mathrm{diff}}$ representing the improvement to the control scheme achieved by allowing for variable-strength measurements; see text. The dashed line shows the cases where ${\overline{F}}_{\mathrm{DN}}={\overline{F}}_H$. Below this line ${\overline{F}}_{\mathrm{DN}}>{\overline{F}}_H$, i.e., the Helstrom scheme ($H$) performs worse than doing nothing at all. This clearly emphasizes that strong measurements are not generally appropriate for the control of quantum systems.Reuse & Permissions

Figure 3

Experimental results of our quantum feedback control procedure. (a) Fidelities between input and output states [Eqs. (2, 3)], as a function of measurement strength ($\cos \chi$). The model is discussed in the text. Error bars are calculated from Poissonian photon counting statistics. (b) Corresponding output states presented as vectors on the Bloch sphere. Light gray vectors are those predicted by the experimental model, as in (a). The colored vectors correspond to colored points in (a), and the corresponding measurement strength is shown next to each vector.Reuse & Permissions