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Quantum key distribution (QKD) enables two remote parties to share encryption keys with security based on the laws of physics. Continuous-variable (CV) QKD with coherent states and coherent detection integrates well with existing telecommunication networks. Thus far, long-distance CV-QKD has only been demonstrated using a highly complex scheme where the local oscillator is transmitted, opening security loopholes for eavesdroppers and limiting potential applications. Here, we report a long-distance CV-QKD experiment with a locally generated local oscillator over a 100-kilometer fiber channel with a total loss of 15.4 decibels. This record-breaking distance is achieved by controlling the phase noise-induced excess noise through a machine learning framework for carrier recovery and optimizing the modulation variance. We implement the full CV-QKD protocol and demonstrate the generation of keys secure against collective attacks in the finite-size regime. Our results mark a substantial milestone for realizing CV quantum access networks with a high loss budget and pave the way for large-scale deployment of secure QKD.

We investigated a machine learning method for joint estimation of polarization and phase for use in a Gaussian modulated CV-QKD system, over an 18 hour period measured on a installed fiber with 5.5 dB attenuation.

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 108 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.

Distributing cryptographic keys over public channels in a way that can provide information-theoretic security is the holy grail for secure communication. This can be achieved by exploiting quantum mechanical principles in so-called quantum key distribution (QKD). Continuous-variable (CV) QKD based on coherent states, in particular, is an attractive scheme for secure communication since it requires only standard telecommunication technology that can operate at room temperature. However, a recently discovered side-channel created in the process of state preparation leads to a leakage of information about the transmitted quantum state, opening a security loophole for eavesdroppers to compromise the security of the CVQKD system. Here, we present a CVQKD system without this modulation leakage vulnerability. Our implementation is based on a baseband modulation approach and uses an in-phase and quadrature (IQ) modulator for state preparation and radio frequency heterodyne detection together with carefully designed digital signal processing for state measurement. We consider practical aspects in the implementation and demonstrate the generation of a composable secret key secure against collective attacks. This work is a step towards protecting CVQKD systems against practical imperfections of physical devices and operational limitations without performance degradation.

Continuous variable quantum key distribution (CV-QKD) is a promising emerging technology for the distribution of secure keys for symmetric encryption. It can be readily implemented using commercial off-the-shelf optical telecommunications components. A key requirement of the CV-QKD receiver is the ability to measure the quantum states at the correct time instance and rate using the correct orthogonal observables, referred to as synchronization. We propose a digital synchronization procedure for a modern CV-QKD system with locally generated local oscillator for coherent reception. Our proposed method is modulation format independent allowing it to be used in a variety of CV-QKD systems. We experimentally investigate its performance with a Gaussian modulated CV-QKD system operating over a 10-20 km span of standard single mode fibre. Since the procedure does not require hardware modifications it paves the way for cost-effective QKD solutions that can adapt rapidly to changing environmental conditions.

Flaws in the process of modulation, or encoding of key bits in the quadratures of the electromagnetic light field, can make continuous-variable quantum key distribution systems susceptible to leakage of secret information. Here, we report such a modulation leakage vulnerability in a system that uses an optical in-phase and quadrature modulator to implement a single sideband encoding scheme. The leakage arises from the limited suppression of a quantum-information-carrying sideband during modulation. Based on the results from a proof-of-concept experiment, we theoretically analyze the impact of this vulnerability and show that the leakage reduces the range over which secret key can be obtained, and can even lead to a security breach, if disregarded. We also study the efficacy of additional trusted noise to counter this vulnerability.

The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the frequency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we explore the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method and a previously demonstrated machine learning method. Experimental results obtained over a 20-km fibre-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. This may enable CV-QKD systems with low hardware implementation complexity which can seamlessly work on diverse transmission lines.

A perspective on how machine learning can aid the next–generation of classical and quantum optical communication systems is given. We focus on the design of Raman amplifiers and phase tracking at the quantum limit.

Spectral purity of laser sources is typically investigated using phase or frequency noise measurements, which require extraction of the optical phase. This is a challenging task if the signal-to-noise-ratio (SNR) of the spectral line or the linewidth-to-noise-ratio (LNR) are not sufficiently high. In this letter, we present a statistically optimal method for optical phase noise measurement that relies on coherent detection and Bayesian filtering. The proposed method offers a record sensitivity, as the optical phase is measured at a signal power of -75 dBm (SNR of -11 dB in 1.1 GHz receiver bandwidth). Practically, this means that the phase noise measurements are, up to a high-degree, not limited by the measurement noise floor. This allows measurements down to -200 dB rad2/Hz and up to 10 GHz, which is useful when measuring the Schawlow-Townes (quantum noise limited) laser linewidth. Finally, the estimated optical phase is highly accurate allowing for quantum limited signal demodulation. The method thus holds the potential to become a reference measurement tool.

Spectral purity of laser sources is typically investigated using phase or frequency noise measurements, which require extraction of the optical phase. This is a challenging task if the signal–to–noise–ratio (SNR) of the spectral line or the linewidth–to–noise–ratio (LNR) are not sufficiently high. In this paper, we present a statistically optimal method for optical phase noise measurement that relies on coherent detection and Bayesian filtering. The proposed method offers a record sensitivity, as the optical phase is measured at a signal power of -75 dBm (SNR of -11 dB in 1.1 GHz receiver bandwidth). Practically, this means that the phase noise measurements are, up to a high–degree, not limited by the measurement noise floor. This allows measurements down to -200 dB rad2/Hz and up to 10 GHz, which is useful when measuring the Schawlow–Townes (quantum noise limited) laser linewidth. Finally, the estimated optical phase is highly accurate allowing for quantum limited signal demodulation. The method thus holds the potential to become a reference measurement tool.