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SPIE Quantum Technologies

Discrete phase CV-QKD over a hybrid free space - fiber channel with K-means clustering

Saravana Vilashini M, Anil Prabhakar

Published Apr 5, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.3014845

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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.
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 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 have developed a continuous-variable quantum key distribution (CV-QKD) system that employs discrete quadrature-amplitude modulation and homodyne detection of coherent states of light. We experimentally demonstrated automated secure key generation with a rate of 50 kbps when a quantum channel is a 10 km optical fibre. The CV-QKD system utilises a four-state and post-selection protocol and generates a secure key against the entangling cloner attack. We used a pulsed light source of 1550 nm wavelength with a repetition rate of 10 MHz. A commercially available balanced receiver is used to realise shot-noise-limited pulsed homodyne detection. We used a non-binary LDPC code for error correction (reverse reconciliation) and the Toeplitz matrix multiplication for privacy amplification. A graphical processing unit card is used to accelerate the software-based post-processing.
Future quantum communication infrastructures will need to serve heterogeneous users on shared physical channels: short-range, high-throughput links favor Continuous-Variable Quantum Key Distribution (CV-QKD), while long-reach, high-loss links remain the domain of Discrete-Variable QKD (DV-QKD). Wavelength-division multiplexing (WDM) of the two protocols on a common channel would address both regimes simultaneously, but their markedly different noise sensitivities make coexistence non-trivial and, to date, experimentally untested. Here we report the first simultaneous operation of two independent CV- and DV-QKD systems on a common optical channel, using standard C-band DWDM filters at 1550.12 nm (CV) and 1545.32 nm (DV). We demonstrate joint operation on both optical fiber and a 620 m urban daylight free-space link. On fiber, the two systems exhibit the expected complementarity, crossing over at 7.56 dB of channel loss where both deliver $\sim$1.43 Mbit/s; in daylight free-space, both sustain Mbit/s key rates under time-varying atmospheric attenuation. Across all configurations we observe no measurable multiplexing-induced penalty in QBER or excess noise. These results establish hybrid CV-DV WDM as a practical building block for heterogeneous quantum communication networks, where metropolitan high-throughput users and long-reach backbone links can be served on a single physical infrastructure.
This paper proposes to design a satellite-based free-space quantum key distribution (QKD) systems using quadrature phase-shift-keying (QPSK) signaling. Our proposed QKD system based on continuous variable encoding to provide the secret-key transmission, where the key information is encoded on four coherent states corresponding to QPSK modulation scheme. In addition, we use heterodyne detection receiver to improve the receiver sensitivity thus decode the signal with high fidelity. The performance of the proposed free-space QKD system is analytically investigated. More especially, the mathematical expression for quantum bit error rate (QBER) is derived taking into account the effect of physical layer impairments and parameters. The numerical results help to determine the appropriate values of system's parameters such as the threshold coefficients and the required transmitted power.
Continuous-variable quantum key distribution (CV-QKD) has been proposed as a method for securely exchanging keys to protect against the security concerns caused by potential advancements in quantum computing. In addition to optical fibre transmission, the free-space optical (FSO) channel is an interesting channel for CV-QKD, as it is possible to share keys over this channel wirelessly. The instability of the FSO channel caused by turbulence-induced fading, however, can cause a degradation in the system's performance. One of the most important aspects of CV-QKD is the reconciliation step, which significantly impacts the performance of the CV-QKD system. Hence, rate-adaptive reconciliation is necessary for CV-QKD over FSO to combat the fluctuations in the channel and improve secret key rates (SKRs). Therefore, in this paper, we simulate the impact of discrete modulation on the reconciliation efficiency and consider the use ofddd-dimensional reconciliation withd>8d > 8d>8to mitigate this impact, improving reconciliation efficiencies by up to 3.4%. We validate our results by experimentally demonstrating CV-QKD over a turbulent FSO link and demonstrate SKR gains by up to 165%. Furthermore, we optimise the reconciliation efficiency for FSO links, achieving additional SKR gains of up to 7.6%.