Continuous-variable quantum communication

TL;DR

This review surveys continuous-variable quantum communication, highlighting how phase-space tools and Gaussian-state formalism enable efficient and scalable quantum information exchange. It covers core CV-QKD protocols (coherent/squeezed/entangled, one-/two-/MDI- or thermal-state) and their security analyses, including composable finite-size proofs and Gaussian extremality, alongside practical implementation challenges in fiber and free-space channels. The discussion extends to CV quantum communication beyond QKD—direct communication, dense coding, signatures, authentication, oblivious transfer, teleportation, and GKP-encoded schemes—while also addressing advances in repeaters, post-selection, photonic integration, and channel multiplexing. The paper underscores the practical significance of CV approaches, balancing theoretical rigor with real-world considerations such as device imperfections, side channels, and certification, and points toward future quantum networks leveraging CV-Gaussian tools, non-Gaussian distillation, and GKP encoding for robust, scalable quantum communications.

Abstract

Tremendous progress in experimental quantum optics during the past decades enabled the advent of quantum technologies, one of which is quantum communication. Aimed at novel methods for more secure or efficient information transfer, quantum communication has developed into an active field of research and proceeds toward full-scale implementations and industrialization. Continuous-variable methods of multi-photon quantum state preparation, manipulation, and coherent detection, as well as the respective theoretical tools of phase-space quantum optics, offer the possibility to make quantum communication efficient, applicable and accessible, thus boosting the development of the field. We review the methodology, techniques and protocols of continuous-variable quantum communication, from the first theoretical ideas, through milestone implementations, to the recent developments, covering quantum key distribution as well as other quantum communication schemes, suggested on the basis of continuous-variable states and measurements.

Figures (12)

• Figure 1: CV quantum communication uses wave properties of generally multi-photon light to transmit information by encoding it into conjugate observables of electromagnetic field in the transmitter $A$ and obtaining it from the results of coherent detection in the receiver $B$, enabling, e.g., stronger information security than in classical communication and with potentially higher efficiency compared to single-photon DV quantum communication.
• Figure 2: Left (a): homodyne detection of an incoming signal in mode $s$, based on a balanced coupling with the local oscillator $LO$ and subsequent subtraction and scaling of the signals from the photodetectors (given in grey), resulting in the measured value of an $\hat{x}_s$ or $\hat{p}_s$ quadrature observable of the signal; Right (b): heterodyne (double homodyne) detection of an incoming signal in mode $s$, based on a generally unbalanced splitting coupling to a vacuum mode $vac$ with transmittance $T_\text{het}$ and subsequent measurement of the $\hat{x}_\text{het}$ and $\hat{p}_\text{het}$ quadrature observables, being the linear combinations of the quadratures in modes $s$ and $vac$, by the homodyne detectors on the outputs of the beam splitter (given in blue). The LO modes and the structure of each of the two homodyne detectors (balanced coupling to LO, photocurrent difference scheme), are omitted for simplicity.
• Figure 3: Generic P&M CV-QKD scheme. Alice generates a signal state using the Source, applies the displacement according to the pre-generated data $x_M,p_M$ on the Modulator, and sends the modulated states through the Quantum channel to the remote party Bob, who performs the heterodyne detection with balancing $T_\text{hetB}$, obtaining his data from the measurement of $\hat{x}_B,\hat{p}_B$. The trusted parties then use the authenticated Classical channel to perform error correction and privacy amplification.
• Figure 4: Generic EB CV-QKD scheme. Alice generates a two-mode entangled state using the source EPR (a TMSV state in practice), performs the heterodyne detection on her mode $A$ with balancing $T_\text{hetA}$, obtaining her data from the measurement of $\hat{x}_A,\hat{p}_A$ and sends the mode $B$ through the Quantum channel to the remote party Bob, who performs the heterodyne detection with balancing $T_\text{hetB}$, obtaining his data from the measurement of $\hat{x}_B,\hat{p}_B$. The trusted parties then use the authenticated Classical channel to perform error correction and privacy amplification.
• Figure 5: CV-MDI-QKD scheme. Alice and Bob generate their signal states using each their own source (SA and SB) and perform modulation to encode their data on a respective modulator (MA and MB). The modulated signal travels through the quantum channels (QCA and QCB) to the middle station, where they are coupled on a balanced beam splitter with transmittance $1/2$, the outputs $\hat{x}_-$ and $\hat{p}_+$ are measured and classically broadcasted. The trusted parties then use the authenticated classical channel to perform error correction and privacy amplification.