High-bit-rate continuous-variable quantum key distribution

Quantum key distribution (QKD) [1] has been the most studied quantum information technology primitive for the past twenty years. In a practical QKD protocol, Alice and Bob can extract an arbitrary amount of secret key using an untrusted physical channel (also called a quantum channel), provided a few minimum assumptions such as they have access to a public authenticated channel. Contrary to classical cryptographic primitives whose security can be established only against some restrictive classes of eavesdroppers, QKD keys are secure in the information-theoretic sense even against an eavesdropper with unlimited computational resources or with undisclosed cryptanalytic knowledge. In discrete-variable (DV) QKD protocols, the information is encoded on discrete values, such as the phase or the polarization of single photons, and detection is done using single-photon detectors. Continuous-variable (CV) QKD protocols employ continuous or discrete modulations [2] of the quadratures of the electromagnetic field. CVQKD setups rely on a coherent detection (homodyne or heterodyne) between the quantum signal and a classical reference signal called the local oscillator, and their implementation requires only standard telecom components. They are compatible with wavelength division multiplexing [3], which greatly eases their deployment into telecommunication networks. In the early history of CVQKD, this technology was expected to achieve higher secret key rates than DVQKD protocols thanks to the possibility of encoding more than 1 bit per pulse. However, the secure distance of the most common CVQKD protocol [4], which consists of a Gaussian modulation of coherent states in the phase space and a homodyne detection of any of two orthogonal quadratures of the field at random, was limited to 25 km [5] for a long time because of the lack of efficient error correction procedures at low signal-to-noise ratios. This problem was solved thanks to the multidimensional reconciliation technique proposed in [6] together with the design of high-efficiency error correcting codes in [7] and significantly extended the secure distance of CVQKD to about 80 km [8]. However, multidimensional protocols are limited to 1 bit per pulse. In this paper, we exhibit high-efficiency error correcting codes for the additive white Gaussian noise channel (AWGNC). In the high signal-to-noise ratio (SNR) regime, it allows us to go beyond previous achievable secret key rates [8] with CVQKD systems and extract more than 1 bit of secret key per channel use, a rate impossible to attain, even in principle, with qubit DVQKD systems. In Sec. II, we explain the links between the secret key rate and error correction in CVQKD and review previous work on error correction for both DVQKD and CVQKD. In Sec. III we detail the principle of slice reconciliation, which is a technique that can be used to reconcile nonbinary elements, and study its practical performance in the specific case of the distribution of Gaussian elements. Finally, we show in Sec. IV the consequences of these developments on the performance of the Gaussian protocol over short distances with a state-of-the-art CVQKD system and make projections about future achievable secret key rates.