Figure 5: Server implementing a squeezing gate.

(a) Experimental setup. The squeezing gate was implemented by injecting the input states into a squeezed light source made of a periodically poled potassium titanyl phosphate in a linear cavity. After squeezing, the output state was sent back to the client who decrypted it by interfering the mode with another beam that was modulated with π-phase shifted encryption noise at a 2% tap-off beam splitter. Owing to squeezing the amplitude quadrature, the decryption noise was amplified differently in the two quadratures with gains g₁ and g₂ depending on the squeezing strength. More details can be found in Supplementary Methods. (b) The fidelity between the output states of the computation on encrypted and plain-text states with both 100% channel transmission and 5 dB transmission loss corresponding to optical loss in 10 km fibre at telecom wavelength. Statistical error bars are smaller than the point size. The variation of the fidelities comes mainly from systematic errors in the fine tuning of the decryption and system drifts. (c–f) Reconstructed Wigner functions in phase space for each step in the protocol with a coherent input state and the squeezing gate measured by homodyne detection after each step at a side-band frequency of 10.5 MHz. The black circle in f denotes the full width at half maximum (FWHM) of the ideal squeezing ellipse. (g) Shows the signal-to-noise ratios in the Q and P quadratures for the states shown in panels c–f as well as for an output state that was not encrypted during computation. The dashed lines indicate the signal-to-noise ratio of an output state using an ideal gate and no channel loss.