Quantum key distribution (QKD) using weak coherent states and homodyne detection is a promising candidate for practical quantum‐cryptographic implementations due to its compatibility with existing telecom equipment and high detection efficiencies. However, despite the actual simplicity of the protocol, the security analysis of this method is rather involved compared to discrete‐variable QKD. This article reviews the theoretical foundations of continuous‐variable quantum key distribution (CV‐QKD) with Gaussian modulation and rederives the essential relations from scratch in a pedagogical way. The aim of this paper is to be as comprehensive and self‐contained as possible in order to be well intelligible even for readers with little pre‐knowledge on the subject. Although the present article is a theoretical discussion of CV‐QKD, its focus lies on practical implementations, taking into account various kinds of hardware imperfections and suggesting practical methods to perform the security analysis subsequent to the key exchange. Apart from a review of well‐known results, this manuscript presents a set of new original noise models which are helpful to get an estimate of how well a given set of hardware will perform in practice.

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines1,2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing3, in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity5, using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 μs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

We present a pilot-assisted coherent intradyne reception methodology for CV-QKD with true local oscillator.An optically phaselocked reference tone, prepared using carriersuppressed optical single-sideband modulation, is multiplexed in polarisation and frequency to the 250 Mbaud quantum signal in order to provide optical frequency-and phase matching between quantum signal and local oscillator. Our concept allows for high symbol rates and can be operated at an extremely low excess-noise level, as validated by experimental measurements.