Fig. 1: General concept of a prepare-and-measure CV-QKD protocol based on displaced squeezed states and its microwave experimental implementation.

a In the CV-QKD protocol, Alice encodes her key \({{{\mathcal{K}}}}_{{{\rm{A}}}}={\left\{{\alpha }_{i}\right\}}_{i\in \left\{1,\ldots,N\right\}}\) in an ensemble of q- or p-displaced squeezed states. These states propagate as microwave signals through a quantum channel, which is assumed to be under Eve’s control and is parametrized by power losses ε_E and an added noise photon number \(\bar{n}\). Bob performs SQMs to extract displacement amplitudes of each incoming state, resulting in a measured key \({{{\mathcal{K}}}}_{{{\rm{B}}}}={\left\{{\beta }_{i}\right\}}_{i\in \left\{1,\ldots,N\right\}}\) (see Supplementary Notes 2 and 3). b Experimental scheme of the microwave CV-QKD protocol with superconducting JPAs in the cryogenic environment. For each symbol, Alice generates a q- or p-squeezed state which is subsequently displaced using a directional coupler coupled to a strong coherent signal. The resulting state propagates through a quantum channel consisting of a second directional coupler with transmissivity 1 − ε_E = 0.9885. This coupler is used to inject a variable number of noise photons \(\bar{n}\) and, thus, simulate different channel conditions. On Bob’s side, a strong phase-sensitive amplification is performed using a second JPA, resulting in the SQM of each received microwave signal. Each of these signals is sampled using a field-programmable gate array (FPGA) to compute a single I/Q point from which the displacement β_i is obtained. Color plots in boxes depict Wigner functions of quantum states in the quadrature phase space (q, p). c Legend for various experimental components in (b).