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Sensors

Enhancing Performance of Continuous-Variable Quantum Key Distribution (CV-QKD) and Gaussian Modulation of Coherent States (GMCS) in Free-Space Channels under Individual Attacks with Phase-Sensitive Amplifier (PSA) and Homodyne Detection (HD)

Nancy Alshaer, Tawfik Ismail, Haitham Mahmoud

Published Aug 11, 2024• 9 citations
Publisher

Abstract

In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.

DOI
10.3390/s24165201

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In recent research, there has been a significant focus on establishing robust quantum cryptography using the continuous-variable quantum key distribution (CV-QKD) protocol based on Gaussian modulation of coherent states (GMCS). Unlike more stable fiber channels, one challenge faced in free-space quantum channels is the complex transmittance characterized by varying atmospheric turbulence. This complexity poses difficulties in achieving high transmission rates and long-distance communication. In this article, we thoroughly evaluate the performance of the CV-QKD/GMCS system under the effect of individual attacks, considering homodyne detection with both direct and reverse reconciliation techniques. To address the issue of limited detector efficiency, we incorporate the phase-sensitive amplifier (PSA) as a compensating measure. The results show that the CV-QKD/GMCS system with PSA achieves a longer secure distance and a higher key rate compared to the system without PSA, considering both direct and reverse reconciliation algorithms. With an amplifier gain of 10, the reverse reconciliation algorithm achieves a secure distance of 5 km with a secret key rate of 10-1 bits/pulse. On the other hand, direct reconciliation reaches a secure distance of 2.82 km.
Future global quantum communication networks, or quantum internet, will realize high-rate secure communication and entanglement distribution for large-scale users over long distances. Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach high rates. However, the achievable performance of CV-QKD protocols is fundamentally limited by the fact that they appear to be fragile to both loss and noise. In this study, we provide a general framework for analyzing the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state (GMCS) protocol under various levels of trust for the loss and noise experienced by the users of the protocol. Our work is comprehensive of several practical scenarios, encompassing both active and passive eavesdropping configurations, with both wired (i.e., fiber-based) and wireless (i.e., free-space and satellite-based) quantum communication channels. Our numerical results evaluate the robustness of the GMCS protocol under varying levels of trust and demonstrate that it is difficult for a practical protocol to remain robust against untrusted loss at the transmitter. In the wireless case, we analyze a scenario with a sun-synchronous satellite, showing that its key distribution rate, even with the worst level of trust, can outperform a ground chain of ideal quantum repeaters. Our results indicate that—when it comes to engineering and optimizing quantum-safe networks—it is essential to mitigate the shortcomings caused by critical trade-offs between rate performance, trust level, system noise, and communication distance.
Abstract Transmission losses through optical fibers are one of the main obstacles preventing both long-distance quantum communications and continuous-variable quantum key distribution. Optical amplification provides a tool to obtain, at least partially, signal restoration. In this work, we address a key distribution protocol over a multi-span link employing either phase-insensitive (PIA) or phase-sensitive (PSA) amplifiers, considering Gaussian modulation of coherent states followed by homodyne detection at the receiver’s side. We perform the security analysis under both unconditional and conditional security frameworks by assuming in the latter case only a single span of the whole communication link to be untrusted. We compare the resulting key generation rate (KGR) for both kinds of amplified links with the no-amplifier protocol, identifying the enhancement introduced by optical amplification. We prove an increase in the KGR for the PSA link in the unconditional scenario and for both PSA and PIA in the conditional security setting depending on position of the attack and the measured quadrature.
We evaluate the performance of Gaussian Modulated Coherent State (GMCS) Continuous-Variable Quantum Key Distribution (CV-QKD), in terms of secure key rate, at different detector bandwidths. We illustrate the advantages and limitations of high-speed CV-QKD systems using a general noise model in which we consider various noise sources and their dependence upon detection bandwidth. Experimentally, the feasibility of high speed CV-QKD is demonstrated by using a GHz bandwidth balanced homodyne detector (BHD) established with commercially available components. We provide secure key rates of transmitted and local local oscillator schemes under various clock rates.
We experimentally demonstrated a sub-Mbps key rate Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) over a 100-km transmission distance. To efficiently control the excess noise, the quantum signal and the pilot tone are co-transmitted in the fiber channel based on wideband frequency and polarization multiplexing methods. Furthermore, a high-accuracy data-assisted time domain equalization algorithm is carefully designed to compensate the phase noise and polarization variation in low signal-to-noise ratio. The asymptotic secure key rate (SKR) of the demonstrated CV-QKD is experimentally calculated to be 7.55 Mbps, 1.87 Mbps, and 0.51 Mbps over a transmission distance of 50 km, 75 km, and 100 km, respectively. The experimentally demonstrated that the CV-QKD system significantly improves the transmission distance and SKR compared to the state-of-art GMCS CV-QKD experimental results, and shows the potential for long-distance and high-speed secure quantum key distribution.
Abstract Self-referenced continuous-variable quantum key distribution (SR-CVQKD) protocols, which operate with a real local local oscillator (LLO) at the receiver side, provide the major advantage that they can defend against all attacks associated with the local oscillator. We propose a method to enhance the performance of the SR-CVQKD by adding an optical parametric amplifier into the receiver’s apparatus. Considering reverse reconciliation, the secret key rate against collective eavesdropping attacks is calculated. For the plug-and-play dual-phase-modulated coherent-states (DPMCS) SR-CVQKD protocol, we demonstrate that an ideal phase-sensitive amplifier (PSA) can enhance the efficiency of a homodyne detector, and the compensation ability of a realistic phase-insensitive amplifier (PIA) for heterodyne detection varies according to different values of N, which indicates the noise variance of the PIA. Moreover, these arrangements of optical amplifiers also have applications in one-way SR-CVQKD systems.
We propose a simplified measurement scheme for a Gaussian modulated coherent state (GMCS) protocol for continuous variable quantum key distribution (CV-QKD), utilizing homodyne detection without quadrature switching. The reference frame of measurement is taken to be at an arbitrary angle, however, reconciliation converges the proposed scheme to GMCS with switching quadrature protocol. The arbitrary frame of measurement could also include the unknown random thermal drift within Bob's optical measurement setup. We found this scheme is advantageous for practical free-space and fiber-based GMCS protocol-based CV-QKD systems as it does not require a phase modulator for random measurement selection quadrature at Bob.