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.
Encoding of key bits in the quadratures of the electromagnetic light field is an essential part of any continuousvariable quantum key distribution system. However, flaws of practical implementation can make such systems susceptible to leakage of secret information. We verify a side channel presence in an optical in-phase and quadrature modulator which is caused by limited suppression of a quantum information-carrying sideband. We investigate various strategies an unauthorized third party can exploit the vulnerability in a proof-of-concept experiment and theoretically assess the modulation leakage effect on a security of the Gaussian coherent-state continuous-variable quantum key distribution protocol and show that the leakage reduces the range of conditions which support secure key generation. Without the control of sideband modulation in practical in-phase and quadrature modulator-based systems the security can be compromised.
Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis.
Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks.
It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied.
We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations.
The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.
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