Figure 1: Conceptual diagram and purification of our QKD protocol.

(a) Alice prepares a conditionally squeezed state by randomly measuring the amplitude or the phase quadratures of one mode of an EPR state using a homodyne detector. The conditionally squeezed state is modulated further by a modulator (Mod) fed with a Gaussian white noise (WN) source controlled by Alice. The homodyne data and the white noise data are stored for signal processing (SP) and the gain between them is optimized. The modulated conditionally squeezed state is transmitted through an untrusted quantum channel where Eve is allowed to perform any attack that mimics the channel transmission η and the channel excess noise ɛ. After the channel Bob performs quadrature measurements using a homodyne detector and the classical post-processing can begin. (b) Purification scheme for an arbitrary Gaussian QKD protocol. Two quadrature squeezers (SQZ₁ and SQZ₂) are placed inside a Mach–Zehnder interferometer with beam splitters of transmittances T₁ and T₂ and fed with modes from two independent EPR sources (EPR₁ and EPR₂). The resulting 4-mode state (A, B, C and D) is pure, whereas the six free parameters can be set so that the two modes A and B can simulate any Gaussian two-mode state (up to a local unitary transformation) including the states produced in our experimental set-up. One mode of the state is measured by an ideal detector at Alice while the other travels through the channel, which has transmission η and excess noise ɛ. Finally Bob's noisy detection is purified by placing a beamsplitter with an EPR input and a transmission mimicking his electronic noise, detection efficiency and the noise he adds to his data, before an ideal detector.