We test a continuous variable quantum key distribution (CV-QKD) protocol using coherent states modulated on a 21.1 MHz sideband of a 1550nm fibre laser (Koheras C15) and demonstrate positive secret keyrates over a lossy channel in a tabletop experiment. Based on analysis for a GG02 protocol, we estimate a maximum keyrate with introduced loss of 1.03 +/- 0.17 bits/pulse at 4.5 dB loss on the X quadrature with a modulation variance of 5.2 SNU and a modulation bandwidth of 500-800 kHz. We observed positive keyrates at 0dB loss for all modulation bandwidths, with distinct peaks at lower modulation variances of approximately 0-5 SNU and 30 SNU for most modulation bandwidths. With introduced loss, the experiment produced positive keyrates on both quadratures for 500kHz modulation bandwidth at 1.4 dB loss, and on the X quadrature for 800kHz modulation bandwidth at 4.5 dB loss. Negative but near zero keyrates were also observed for 600kHz and 1 MHz modulation bandwidths, which may warrant further investigation using different filtering regimes. Digital filtering yielded significant improvements, producing both higher overall keyrates and a much greater number of positive keyrates for filtered versus unfiltered key data. Additional noise or filtering is needed to consistently produce positive keyrates. We identified significant noise on the P quadrature, which limits the viability of using this experiment for a switching protocol. We determined the P quadrature of the laser was not shot noise limited below 15 MHz, with intermittent noise above this from an unknown source. Without further reducing the noise on the P quadrature, it will remain a significant barrier to testing improvements from adaptive optics on this experiment.
We test a continuous variable quantum key distribution (CV-QKD) protocol using coherent states modulated on a 21.1 MHz sideband of a 1550nm fibre laser (Koheras C15) and demonstrate positive secret keyrates over a lossy channel in a tabletop experiment. Based on analysis for a GG02 protocol, we estimate a maximum keyrate with introduced loss of 1.03 +/- 0.17 bits/pulse at 4.5 dB loss on the X quadrature with a modulation variance of 5.2 SNU and a modulation bandwidth of 500-800 kHz. We observed positive keyrates at 0dB loss for all modulation bandwidths, with distinct peaks at lower modulation variances of approximately 0-5 SNU and 30 SNU for most modulation bandwidths. With introduced loss, the experiment produced positive keyrates on both quadratures for 500kHz modulation bandwidth at 1.4 dB loss, and on the X quadrature for 800kHz modulation bandwidth at 4.5 dB loss. Negative but near zero keyrates were also observed for 600kHz and 1 MHz modulation bandwidths, which may warrant further investigation using different filtering regimes. Digital filtering yielded significant improvements, producing both higher overall keyrates and a much greater number of positive keyrates for filtered versus unfiltered key data. Additional noise or filtering is needed to consistently produce positive keyrates. We identified significant noise on the P quadrature, which limits the viability of using this experiment for a switching protocol. We determined the P quadrature of the laser was not shot noise limited below 15 MHz, with intermittent noise above this from an unknown source. Without further reducing the noise on the P quadrature, it will remain a significant barrier to testing improvements from adaptive optics on this experiment.
We present a discretely modulated continuous-variable quantum key distribution system in free space by using strong coherent states. The amplitude noise in the laser source is suppressed to the shot-noise limit by using a mode cleaner combined with a frequency shift technique. Also, it is proven that the phase noise in the source has no impact on the final secret key rate. In order to increase the encoding rate, we use broadband homodyne detectors and the no-switching protocol. In a realistic model, we establish a secret key rate of 46.8 kbits/s against collective attacks at an encoding rate of 10 MHz for a 90 channel loss when the modulation variance is optimal.
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.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
Quadrature Phase Shift Keying Continuous Variable Quantum Key Distribution (QPSK CV-QKD) can be used to encode bits of information on weak coherent states, enhanced with quantum scissors. In our experiment, we use discretely modulated QPSK CV-QKD across a 150 m long Free-Space Optical (FSO) link over the two buildings with a four-symbol constellation. Other CV-QKD deployments in the literature have demonstrated a Frame Error Rate of 20% with a 100 MHz repetition rate and a loss of 6 dB in the channel. Our setup has a QBER of 25% for a 35 dB channel loss. Our system has been tested for a link loss of upto 50 dB. The QPSK symbols generated at 100 MHz from a Zynq Ultrascale+ Field Programmable Gated Array and fed to an I/Q transmitter, which in turn modulated a 1550 nm laser. The FSO transmitter, connected to our lab 500 m away, consists of a collimator and a beam expander. The transmitted states were captured on the other side by a FSO receiver unit consisting of a collimator. The received signal was transported back to the lab via a fiber of length 1 km, which is then passed through a 90 degree hybrid coherent receiver, with a 1 GHz bandwidth. The captured quadratures are post processed with a k-means cluster algorithm allowing us to recover the bit values. Our experiments focus on understanding the change in BER in the presence of varying levels of attenuation over the hybrid FSO+fibre channel.
The aim of this thesis is to develop continuous variable quantum key distribution (CVQKD) for the goal of securing a global quantum network. A numerical tool was developed for comparing different CVQKD protocols and identifying parameter spaces for positive and negative secret key rate (SKR) while taking into account the simultaneous effects of CVQKD parameters. Using the transmittance, excess noise, and amplitude modulation, the tool shows that the M-QAM protocol outperforms M-APSK which outperforms M-PSK. In addition, increasing the number of coherent states for a protocol non-linearly increases the capability of a protocol to produce positive SKRs. The tool also identifies parameters spaces, such as small excess noise regimes, where protocols have the same performance. The tool helps identify appropriate protocols for channels where parameters such as the transmittance and excess noise fluctuate, and can be extended to include more CVQKD parameters. The improvement of CVQKD in turbulent channels, through the use of adaptive optics (AO), was studied by investigating the interferometric visibility between a quantum signal and a local local oscillator in turbulent channels. The results showed that the adaptive optics system was able to increase the interferometric visibility and decrease its fluctuations. In the context of free-space CVQKD, these lead to larger positive and more precise SKRs. The structures of existing QKD networks were analysed and shown how they can be fit into a general three-layer QKD network architecture for the endeavour of a global QKD network architecture. The asymptotic and finite size limit SKRs were calculated for different links CVQKD can be used. The results show that CVQKD achieves longer distances in inter-satellite, satellite-to-ground, fibre, and underwater links in order. In addition, the Gaussian modulated (GM) CVQKD protocol with multidimensional (MD) reconciliation outperforms all other protocols studied by producing positive SKRs for longer link distances. The link capacity, a routing metric for secret key distribution, which considers a dynamic SKR based on dynamic links was developed. Its feasibility in simulated CVQKD networks was presented for the aim of spatiotemporal secret key distribution through a CVQKD network.
An experiment evaluating continuous-variable quantum key distribution (CV-QKD) in an urban environment free-space channel has been accomplished using a single homodyne detector. This is based on Gaussian modulation with coherent states in the polarization degree of freedom. We achieved a QKD distance at 460 m at a repetition rate of 10 kHz. The secure key rate is 0.152 kbps at the typical reconciliation efficiency of 0.95. The experimental setup of this scheme is simplified, and the barrier for implementation has been remarkably reduced compared to that for traditional symmetric modulation protocols, for example, the GG02 protocol proposed in F. Grosshans and P. Grangier [Phys. Rev. Lett. 88, 057902 (2002)]. The influence of the security key rate by asymmetric modulation is small for a relatively low channel loss condition in a free-space environment. This scheme is expected to have significance for future practical applications.