In this paper, we explore the enhancement of secure transmission distance in continuous-variable quantum key distribution (CV-QKD) under limited eavesdropping conditions by employing a quantum scissor (QS). We derive an analytical expression for the output state and demonstrate that QS significantly extends the secure communication range. Additionally, we analyze the impact of limited eavesdropping on the secret key rate, showing that restricted access to intercepted light improves security compared to an unrestricted eavesdropper scenario. To provide a comprehensive assessment, we investigate both direct and reverse reconciliation schemes. Our numerical simulations and analytical comparisons reveal that QS improves the secure transmission distance in both cases, despite reducing the secret key rate at shorter distances. The results show that QS mitigates the detrimental effects of channel loss, allowing for an extended communication range in CV-QKD systems. These findings highlight the potential of QS as a key tool for enhancing long-distance secure quantum communication in practical scenarios. • Study of secure-distance enhancement in CV-QKD with limited eavesdropping using a QS. • QS improves the maximum secure transmission distance of the CV-QKD protocol. • Key rates under limited eavesdropping are analyzed for both reconciliation types. • Limited eavesdropping yields higher key rates than the fully unrestricted case. • Optimal modulation variance and QS gain that extend protocol range are identified.
In this paper, we explore the enhancement of secure transmission distance in continuous-variable quantum key distribution (CV-QKD) under limited eavesdropping conditions by employing a quantum scissor (QS). We derive an analytical expression for the output state and demonstrate that QS significantly extends the secure communication range. Additionally, we analyze the impact of limited eavesdropping on the secret key rate, showing that restricted access to intercepted light improves security compared to an unrestricted eavesdropper scenario. To provide a comprehensive assessment, we investigate both direct and reverse reconciliation schemes. Our numerical simulations and analytical comparisons reveal that QS improves the secure transmission distance in both cases, despite reducing the secret key rate at shorter distances. The results show that QS mitigates the detrimental effects of channel loss, allowing for an extended communication range in CV-QKD systems. These findings highlight the potential of QS as a key tool for enhancing long-distance secure quantum communication in practical scenarios. • Study of secure-distance enhancement in CV-QKD with limited eavesdropping using a QS. • QS improves the maximum secure transmission distance of the CV-QKD protocol. • Key rates under limited eavesdropping are analyzed for both reconciliation types. • Limited eavesdropping yields higher key rates than the fully unrestricted case. • Optimal modulation variance and QS gain that extend protocol range are identified.
Quantum key distribution (QKD) is fundamentally different from most classical key distribution schemes, such as Diffie-Hellman key exchange, in the sense that no computational complexity assumption is required on the power of adversaries to prove its security. QKD relies on basic laws of quantum physics and it is proven that it can enable highly secure data communication. Such achievements, however, are facing technological problems that have to be resolved in order to provide a viable solution to a large group of customers. While there are discrete-variable QKD schemes, which rely on encoding data in discrete degrees of freedom, such as polarization of single photons, in this thesis, we focus on the continuous-variable QKD (CV-QKD) protocols, in which data is encoded on the quadratures of light. Currently, one of the major drawbacks of CV-QKD is its poor performance at long distances. Nevertheless, such a limitation in CV-QKD can be overcome with the assistance of quantum repeaters that rely on entanglement distillation via noiseless linear amplifiers (NLAs). Such systems can, in principle, offer large secret key rates over long distances. In this thesis, we aim to provide a realistic analysis of a CV-QKD protocol running over quantum scissors (QSs) as realistic NLAs. We will report the obstacles that one could face in realizing CV-QKD in such a scenario. A review of CV-QKD and QS-based NLAs will be given, based on which QS-assisted CV-QKD is proposed. We, particularly, focus on the modelling of the QSs' structure and their effect on the secret key rate aiming to find operational regimes where the performance of the QKD scheme is enhanced. This study paves the way for implementing long-distance CV-QKD protocols that rely on QS/NLA devices over CV quantum repeaters. \n \nIn this thesis, we also consider and account for a realistic analysis of a CV-QKD protocol with non-Gaussian modulation, which is assisted by the means of QSs. We will show that, while we have to deal with similar obstacles as in the Gaussian modulation, we can potentially improve performance of the non-Gaussian modulation protocol. \n \nAs an alternative approach to extend the secure distance of CV-QKD protocols, the last part of this thesis is devoted to presenting realistic threat models for satellite QKD, wherein we consider several eavesdropping scenarios by limiting eavesdroppers' access to the trusted ground and/or satellite stations. In such scenarios, the eavesdropper has only limited access to the sender and/or receiver stations. \nFor example, we will explore the case where an eavesdropper can only receive an attenuated version of the transmitted signals. As well, we will focus on the case where Eve's signals would reach the receiver via a lossy channel inaccessible to the eavesdropper. We show that, in the case of both Gaussian and non-Gaussian protocols, this limitation would allow trusted parties to achieve higher key rates than what can be achieved when unrestricted eavesdropping is possible.
Continuous-variable quantum key distribution (CV-QKD) is a promising quantum-safe alternative to classical asymmetric cryptography that enables two authenticated parties to establish a shared secret over a potentially eavesdropped quantum channel. A key step in CV-QKD post-processing is information reconciliation, which leverages forward error correction (FEC) techniques to extract identical bit strings from noisy correlated data. In this work, we analyze the strict limitations on operating distance that are imposed by constant-rate FEC, severely limiting the practicability of CV-QKD systems in deployed optical networks. To overcome the distance limitations, we evaluate three strategies: (i) tuning modulation variance, (ii) adding controlled amounts of trusted detector loss, and (iii) the use of rate-adaptive FEC. All approaches are validated experimentally, compared in terms of performance, and we discuss implementation aspects. Our results show that while methods (i) and (ii) extend the operational distance of constant-rate FEC without the need for additional hardware components, they incur a significant penalty in secret key rate (SKR). In contrast, rate-adaptive FEC enables CV-QKD operation with performance close to the asymptotic SKR over a wide range of distances, provided that the reconciliation efficiency is chosen appropriately.
Summary form only given. The recent progress in continuous-variable quantum key distribution (CV-QKD) systems has placed them in a competitive position with their conventional discrete-variable counterparts [1]. In particular, CV-QKD might be the better choice over short distances. When it comes to long distances, however, the story is different. One of the proposed solutions to improve rate-versus-distance performance is to use noiseless linear amplifiers (NLAs) [2], but a realistic analysis that accounts for non-idealities of existing NLAs is missing. One of the most well-known NLAs is based on quantum scissors (QSs) [3], whose ideal operation relies on the single-photon assumption of its inputs. In this study, we report the exact calculation of the secret key rate for the GG02 protocol [4] that is enhanced by a single QS; see Fig. 1(a). We remove the single-photon assumption in the QS modeling and find regimes of operation where QS-assisted GG02 offers advantages over the conventional GG02 system. Our results imply that the region over which rate enhancement is achieved is limited to the regime of long distances.
It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive.
Quantum key distribution (QKD) can provide unconditional security to next generation communication networks guaranteed by the laws of quantum physics. This paper studies the secret key rate (SKR) of a continuous variable quantum key distribution (CV-QKD) system using multiple-input multipleoutput (MIMO) transmission and operating at Terahertz (THz) frequencies. Distinct from previous works, we consider a practical “restricted" eavesdropping scenario in which Eve can collect only a fraction of photons lost in the environment. We propose a system model for the MIMO THz CV-QKD system that accounts for restricted eavesdropping via a lossy wireless channel between Alice and Eve. We derive for this system new SKR expressions for both coherent-state-based and squeezed-state-based CV-QKD protocols. Our results show that previous analysis assuming unrestricted eavesdropping leads to overly pessimistic SKRs, and that in practice, the achievable SKR can be significantly increased under restricted eavesdropping. The increase in the SKR is quantified by the simplified SKR expansions derived in this paper. Our results also reveal that squeezing is beneficial for improving the SKR only for unrestricted eavesdropping. However, in a practical setting with restricted eavesdropping, increased squeezing leads to a reduction in the SKR.
It is known that quantum scissors, as non-deterministic amplifiers, can enhance the performance of Gaussian-modulated continuous-variable quantum key distribution (CV-QKD) in noisy and long-distance regimes of operation. Here, we extend this result to a non-Gaussian CV-QKD protocol with discrete modulation. We show that, by using a proper setting, the use of quantum scissors in the receiver of such discrete-modulation CV-QKD protocols would allow us to achieve positive secret key rates at high loss and high excess noise regimes of operation, which would have been otherwise impossible. This also keeps the prospect of running discrete-modulation CV-QKD over CV quantum repeaters alive.