Fig. 3: Secret key of the microwave CV-QKD protocol.

a Measured secret key of the CV-QKD protocol for two experimental runs: 1^st with squeezing (anti-squeezing) levels of 3.6 (7.1) dB and 2nd with squeezing (anti-squeezing) levels of 3.6 (7.6) dB. The dashed lines represent the finite-size terms, which impose lowered noise cut-offs for reaching the unconditional security. The error bars and shaded areas denote SD of the experimental data and model, respectively. b Estimation of maximally tolerable losses (solid line) for positive secret keys as a function of the photon number in the thermal background, \({\bar{n}}_{{{\rm{th}}}}\). This analysis is based on the experimental data from the 2nd run. The green shaded area indicates the region of positive (i.e., secure) secret keys. We emphasize two particular temperatures on this curve: the cryogenic temperature ~30 mK and room temperature (RT)  ~ 300 K. At millikelvin temperatures, we assume characteristic losses in superconducting cables of γ = 1.0 × 10⁻³ dB/m while for the open-air conditions, we restrict ourselves to atmospheric microwave losses γ = 6.3 × 10⁻⁶ dB/m due to pure absorption. Under these conditions, we estimate the maximum communication distance, d^* ≃ 1190 m at 30 mK and d^* ≃ 84 m at 300 K. For the open-air scenario, we neglect possible path losses, assuming those can be fully compensated by appropriate antennae, and focus on unavoidable physical limitations.