We address the applicability of quantum key distribution (QKD) with continuous-variable (CV) coherent and squeezed signal states of light over long-distance satellite-based links, considering low Earth orbits in the advantageous downlink scenario and taking into account strong varying channel attenuation (referred to as fading), atmospheric turbulence and finite data ensemble size effects.The study is motivated by the possibility to use highly efficient homodyne detection for CV protocols, which can serve as filter of background radiation due to matching of the quantum signal to a narrowband intense local oscillator beam.Considering feasible Gaussian modulation, compatible with the most advanced security proofs, we obtain tight security bounds on the untrusted excess noise at the channel output, which suggest that the protocols are very sensitive to the channel noise at the respective loss levels.In this regime, either a set-up stabilization resulting in drastic decrease of noise or relaxation of security assumptions to individual or passive collective attacks is required for implementation over the low Earth orbit satellites.Relaxation of security assumptions can be particularly motivated by the possibility of line-of-sight control of the absence of equipment capable of active collective eavesdropping attacks using quantum memories.Furthermore, splitting the satellite pass into discrete segments and extracting the keys from each rather than from the overall single pass allows one to effectively improve robustness against the untrusted channel noise and establish a secure key even under active collective attacks.Such satellite pass segmentation provides another viable option to reduce channel fading thus improving the secure key rate and allowing to establish the secure link with satellites at higher altitudes.We show that the use of signal squeezing can make the protocols more applicable in the satellite links, allowing for higher attenuation and levels of noise at the given security assumptions, and it has to be optimized in the collective attacks scenario.On the other hand, in the case of trusted noise assumption and at high repetition rates, squeezed-state CV QKD can tolerate attenuation levels up to 42 dB, allowing for higher orbit altitudes or smaller receiving telescope apertures.The obtained results are promising for satellite-based QKD, potentially applicable in daylight conditions.
We address the applicability of quantum key distribution (QKD) with continuous-variable (CV) coherent and squeezed signal states of light over long-distance satellite-based links, considering low Earth orbits in the advantageous downlink scenario and taking into account strong varying channel attenuation (referred to as fading), atmospheric turbulence and finite data ensemble size effects.The study is motivated by the possibility to use highly efficient homodyne detection for CV protocols, which can serve as filter of background radiation due to matching of the quantum signal to a narrowband intense local oscillator beam.Considering feasible Gaussian modulation, compatible with the most advanced security proofs, we obtain tight security bounds on the untrusted excess noise at the channel output, which suggest that the protocols are very sensitive to the channel noise at the respective loss levels.In this regime, either a set-up stabilization resulting in drastic decrease of noise or relaxation of security assumptions to individual or passive collective attacks is required for implementation over the low Earth orbit satellites.Relaxation of security assumptions can be particularly motivated by the possibility of line-of-sight control of the absence of equipment capable of active collective eavesdropping attacks using quantum memories.Furthermore, splitting the satellite pass into discrete segments and extracting the keys from each rather than from the overall single pass allows one to effectively improve robustness against the untrusted channel noise and establish a secure key even under active collective attacks.Such satellite pass segmentation provides another viable option to reduce channel fading thus improving the secure key rate and allowing to establish the secure link with satellites at higher altitudes.We show that the use of signal squeezing can make the protocols more applicable in the satellite links, allowing for higher attenuation and levels of noise at the given security assumptions, and it has to be optimized in the collective attacks scenario.On the other hand, in the case of trusted noise assumption and at high repetition rates, squeezed-state CV QKD can tolerate attenuation levels up to 42 dB, allowing for higher orbit altitudes or smaller receiving telescope apertures.The obtained results are promising for satellite-based QKD, potentially applicable in daylight conditions.
We address the applicability of quantum key distribution with continuous-variable coherent and squeezed states over long-distance satellite-based links, considering low Earth orbits and taking into account strong varying channel attenuation, atmospheric turbulence and finite data ensemble size effects. We obtain tight security bounds on the untrusted excess noise on the channel output, which suggest that substantial efforts aimed at setup stabilization and reduction of noise and loss are required, or the protocols can be realistically implemented over satellite links once either individual or passive collective attacks are assumed. Furthermore, splitting the satellite pass into discrete segments and extracting the key from each rather than from the overall single pass allows one to effectively improve robustness against the untrusted channel noise and establish a secure key under active collective attacks. We show that feasible amounts of optimized signal squeezing can substantially improve the applicability of the protocols allowing for lower system clock rates and aperture sizes and resulting in higher robustness against channel attenuation and noise compared to the coherent-state protocol.
With the vastly growing need for secure communication, quantum key distribution (QKD) has been developed to provide high security for communications against potential attacks from the fast-developing quantum computers. Among different QKD protocols, continuous variable (CV-) QKD employing Gaussian modulated coherent states has been promising for its complete security proof and its compatibility with current communication systems in implementation with homodyne or heterodyne detection. Since satellite communication has been more and more important in developing global communication networks, there have been concerns about the security in satellite communication and how we should evaluate the security of CV-QKD in such scenarios. To better analyse the secure key rate (SKR) in this case, in this invited paper we investigate the CV-QKD SKR lower bounds under realistic assumptions over a satellite-to-satellite channel. We also investigate the eavesdropper's best strategy to apply in these scenarios. We demonstrate that for these channel conditions with well-chosen carrier centre frequency and receiver aperture size, based on channel parameters, we can optimize SKR correspondingly. The proposed satellite-based QKD system provides high security level for the coming 5G and beyond networks, the Internet of things, self-driving cars, and other fast-developing applications.
This paper develops a hybrid quantum channel model tailored for finite-regime quantum key distribution (QKD) in free-space satellite quantum communication. The channel model addresses the fading characteristics of satellite-to-ground links while incorporating the dynamics of satellite orbits. By conducting a comprehensive security analysis under finite-size effects and collective attacks, the research bridges the theoretical and practical aspects of satellite-based QKD. Critical parameters, such as reconciliation efficiency, transmission coefficient, detection efficiency, receiver telescope aperture, beam waist, and effective communication time, are systematically investigated to optimize the secret key rate. The study reveals key trade-offs between the influence of satellite altitude on communication windows, noise levels, and synchronization, which significantly impact quantum channel efficiency. The model improves the accuracy of free-space quantum channel evaluations by presenting a hybrid noise framework that combines quantum Poissonian noise with classical additive white Gaussian noise (AWGN). Our numerical results demonstrate the feasibility and robustness of finite-regime QKD for uplink and downlink configurations in various atmospheric conditions, highlighting the superiority of satellite-based quantum communication over conventional networks.
We consider a continuous-variable (CV) quantum key distribution (QKD) protocol over free-space channels, which is simpler and more robust than typical CV QKD protocols. It uses a bright laser, squeezed and modulated in the amplitude quadrature, and self-homodyne detection. We consider a scenario, where the line of sight is classically monitored to detect active eavesdroppers, so that we can assume a passive eavesdropper. Under this assumption, we analyze security of the QKD protocol in the composable finite-size regime. Proper modulation of the squeezed laser to the shot-noise level can completely eliminate information leakage to the eavesdropper and also eliminate the turbulence-induced noise of the channel in the amplitude quadrature. Under these conditions, estimation of the eavesdropper's information is no longer required. The protocol is extremely robust to modulation noise and highly loss-tolerant, which makes it a promising candidate for satellite-based continuous-variable quantum communication.
Currently, quantum key distribution (QKD) using continuous variable (CV) technology has only been demonstrated over short-range terrestrial links. Here, we attempt to answer whether CV-QKD over the much longer satellite-to-Earth channel is feasible. To this end, we first review the concepts and technologies that will enable CV-QKD over the satellite-to-Earth channels. We then consider, in the infinite key limit, the simplest-to-deploy QKD protocols, the coherent state (CS) QKD protocol with homodyne detection and the CS-QKD protocol with heterodyne detection. We then focus on the CS-QKD protocol with heterodyne detection in the pragmatic setting of finite keys, where complete security against general attacks is known. We pay particular attention to the relevant noise terms in the satellite-to-Earth channel and their impact on the secret key rates. In system set-ups where diffraction dominates losses, we find that the main components of the total excess noise are the intensity fluctuations due to scintillation, and the time-of-arrival fluctuations between signal and local oscillator. We conclude that for a wide range of pragmatic system models, CS-QKD with information-theoretic security in the satellite-to-Earth channel is feasible.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.