Fig. 2: Tomography and single-shot measurement histograms of displaced squeezed microwave states.

a Exemplary reconstructed Wigner function of the evolution of a quantum key symbol, starting from its preparation at Alice, followed by propagation through the quantum channel while being exposed to losses and noise (Eve’s attack), finishing at Bob with a strong phase-sensitive amplification. The inset of the left Wigner function plot shows the 1/e contours for an ideal vacuum (red circle) and experimental squeezed state (blue ellipsoid) indicating squeezing below the level of vacuum fluctuations. b Exemplary measured histograms for Alice’s and Bob’s key symbols. For comparison with the measured probability distribution \({P}_{{{\rm{e}}}}\left({X}_{{{\rm{B}}}}\right)\), we plot our quadrature model (solid lines) resulting in a zero-mean Gaussian probability distribution \({P}_{{{\rm{m}}}}\left({X}_{{{\rm{B}}}}\right)\), whose variances are obtained from independent calibration measurements (see “Methods”). c MI between Alice’s and Bob’s keys for the amplified (deamplified) quadrature X_B\(\left({Y}_{{{\rm{B}}}}\right)\) as a function of the coupled noise photon number \(\bar{n}\). We additionally show the MI computed from our model, which is also based on the independent calibration measurements. We emphasize that the model is not a fit of the measurement data. Lastly, we show the corresponding Holevo quantity. The shaded green (red) area on the left (right) represents the region where the MI is larger (smaller) than the Holevo quantity, resulting in a unconditionally secure (insecure) communication. The error bars denote SD of the experimental data.