Optical Continuous-Variable Qubit

In a new branch of quantum computing, information is encoded into coherent states, the primary carriers of optical communication. To exploit it, quantum bits of these coherent states are needed, but it is notoriously hard to make superpositions of such continuous-variable states. We have realized the complete engineering and characterization of a qubit of two optical continuous-variable states. Using squeezed vacuum as a resource and a special photon-subtraction technique, we could with high precision prepare an arbitrary superposition of squeezed vacuum and a squeezed single photon. This could lead the way to demonstrations of coherent state quantum computing.

Figure 1

Experiment outline. (a) Conceptual schematic. (b) Experimental setup. OPO, optical parametric oscillator; $R$, beam splitter reflectivity; LO, local oscillator; APD, avalanche photodiode. See text for details.

Figure 2

Control of superposition weight. A variety of experimentally generated superposition states where the superposition weight $\theta$ has been swept with the phase $\varphi$ fixed at (a) 0° and (b) $-90°$. The upper panels show the Wigner function as a contour plot where the axes are the $x$ and $p$ quadratures. The lower panels show a flattened Bloch sphere with an overlay signifying the fidelity between an ideal qubit [Eq. (2)] at the given ($\theta ,\phi$) point and the measured state. The central longitude corresponds to $\phi =0°$, and $\theta =0°$ at the north pole. The small circles serve to point out which state we were aiming at. The ideal qubit is taken to have a squeezing parameter $r=0.38$.

Figure 3

Control of superposition phase. Generated states with the superposition phase $\varphi$ swept while keeping the superposition weight $\theta$ constant at (a) 135° and (b) 60°.

Figure 4

Influence of displacement strength. Experimentally obtained superposition weights (filled points and solid curves, left axis) and fidelities with the intended target states (unfilled points and dashed curves, right axis) versus the APD count rate of displacement photons relative to squeezing photons for two series of measurements with different superposition phase factor. The curves are obtained from a theoretical model with no free parameters. Note that the extreme data points correspond to count rate ratios of 0 and infinity.