Abstract We propose the Gaussian continuous-variable quantum key distribution using squeezed states in the composite channels including atmospheric propagation with transmittance fluctuations. We show that adjustments of signal modulation and use of optimal feasible squeezing can be sufficient to significantly overcome the coherent-state protocol and drastically improve the performance of quantum key distribution in atmospheric channels, also in the presence of additional attenuating and noisy channels. Furthermore, we consider examples of atmospheric links of different lengths, and show that optimization of both squeezing and modulation is crucial for reduction of protocol downtime and increase of secure atmospheric channel distance. Our results demonstrate unexpected advantage of fragile squeezed states of light in the free-space quantum key distribution applicable in daylight and stable against atmospheric turbulence.
Abstract We propose the Gaussian continuous-variable quantum key distribution using squeezed states in the composite channels including atmospheric propagation with transmittance fluctuations. We show that adjustments of signal modulation and use of optimal feasible squeezing can be sufficient to significantly overcome the coherent-state protocol and drastically improve the performance of quantum key distribution in atmospheric channels, also in the presence of additional attenuating and noisy channels. Furthermore, we consider examples of atmospheric links of different lengths, and show that optimization of both squeezing and modulation is crucial for reduction of protocol downtime and increase of secure atmospheric channel distance. Our results demonstrate unexpected advantage of fragile squeezed states of light in the free-space quantum key distribution applicable in daylight and stable against atmospheric turbulence.
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.
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.
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.
Quantum networks will combine optical fibre with free-space links, yet continuous-variable quantum key distribution (CV-QKD) has been developed predominantly for one medium or the other, while operation across concatenated fibre-free-space channels remains largely unexplored. The two media impose contrasting requirements: fibre transmission is stable and permits long processing intervals, whereas atmospheric propagation imposes transmittance fluctuations that degrade security and must be resolved on short timescales. Here we demonstrate a locally generated local oscillator CV-QKD with both Gaussian-modulated coherent and squeezed states over a deployed hybrid channel comprising a 620-m free-space link and 2 km of deployed fibre, with a total loss up to 20 dB. Rather than adapting the optics to each medium, we move channel adaptation to the post-processing, through a unified adaptive post-processing framework coupling transmittance-based clustering, residual-fading mitigation by covariance-matrix averaging or de-fading, and rate-adaptive blind reconciliation, which alone recovers up to 19% additional key. The same adaptive-processing principle is applied to both protocols, while accounting for their different security analyses and statistical requirements, yielding asymptotic secret-key rates of 0.42 Mbit per sec for the coherent-state protocol and 0.93 Mbit per sec for the squeezed-state protocol under the respective channel conditions, and establishing squeezed-state CV-QKD over a deployed atmospheric channel. These results show that adaptation to the transmission medium can largely be transferred to the data-processing layer, providing a route towards heterogeneous quantum networks spanning fibre, terrestrial free-space and satellite links.
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.
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.