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.
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.
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.
In a practical quantum communication system, the security of signal source of continuous-variable quantum key distribution may be jeopardized due to device flaws and hidden attacks. In this paper, an improved scheme for Gaussian-modulated continuous-variable quantum key distribution based on an untrusted entangled source is proposed. In particular, the entanglement source is placed in an untrusted quantum channel to simulate that it is controlled by an eavesdropper, thereby verifying the security of Gaussian-modulated continuous-variable quantum key distribution in a complex environment. This work in detail analyzes the influence of untrusted entanglement source on practical Gaussian-modulated continuous-variable quantum key distribution system, and the numerical simulation shows that the performance of Gaussian-modulated continuous-variable quantum key distribution will dramatically decrease once the entanglement source has moved out of the sender, and it will slightly rise as the untrusted entanglement source slowly moves away from the sender. This paper further introduces two kinds of optical amplifiers, which are phase-sensitive amplifier and phase-insensitive amplifier, to compensate for the imperfection of the coherent detector. These amplifiers are beneficial to enhancing the quantum efficiency of the receiver’s detector. Specifically, the security key rate of Gaussian-modulated continuous-variable quantum key distribution with homodyne detection can be well improved by phase-sensitive amplifier, and the security key rate of Gaussian-modulated continuous-variable quantum key distribution with heterodyne detection can be well improved by phase-insensitive amplifier. To summary, this paper proposes a scheme for Gaussian-modulated continuous-variable quantum key distribution with untrusted entanglement source, experimental results show that the proposed scheme can generate secure quantum keys even if the Gaussian entanglement source is untrusted, and the two optical amplifiers can effectively improve the quantum efficiency of the detector at the receiver. This work aims to promote the practical process of the Gaussian-modulated continuous-variable quantum key distribution system and provide theoretical guidance for the practical implementation and application of the Gaussian-modulated continuous-variable quantum key distribution system.
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.
Abstract The type of system employing continuous variables, such as light field quadrature for signal modulation, is an important branch for quantum key distribution. Achieving a high key rate using quantum key distribution technology is beneficial for realizing more frequent key updates or enabling one-time pad encryption for high-speed communication tasks. However, the deficiencies of typical large-bandwidth balanced photodetectors prevent the continuous variable quantum key distribution from matching the speed of state-of-the-art classical optical communications. Previous attempts to improve the key rate have focused on designing and manufacturing high-speed balanced photodetectors. It is well known that phase-sensitive amplifiers also improve the performance of balanced photodetectors and thus the performance of key distribution, but the concept remains purely theoretical. Here, for the first time, we experimentally demonstrate a high-speed continuous-variable quantum key distribution operating with a 10 GHz balanced photodetector enhanced by phase-sensitive amplification and detection. A conjugated multi-mode continuous variable protocol is used to accommodate the phase-sensitive operations. The optical amplifier offers a 10 dB increase in the photodetector’s clearance (quantum noise over electrical noise) and improves the detection efficiency from 72% to 96%, thus enabling an overall 248.9 Mb/s key distribution rate through a 16.7 km field-deployed optical fiber.
Nowadays, quantum communications provide a vast field of research in rapid expansion, with a huge potential impact on the future developments of quantum technologies. In particular, continuous variable systems, employing coherent-state encoding and quadrature measurements, represent a suitable platform, due to their compatibility with both the modulation and detection systems currently employed in standard fiber-optical communications. In this work, we address some relevant aspects of the field, and provide innovative results being also experimentally oriented. In particular, we focus on two relevant paradigms: quantum decision theory and continuous variable quantum key distribution (CVQKD). In the former case, we address the problem of coherent-state discrimination and design new hybrid receivers for binary phase-shift keying discrimination, obtaining a quantum advantage over conventional detection schemes, being also robust against typical experimental imperfections. In the latter scenario, we proceed in two different directions. On the one hand, we design new CVQKD protocols employing discrete modulation of coherent states, being a feasible solution compatible with the state of the art in optical communications technologies. On the other hand, we address the more fundamental problem of performing channel losses mitigation to enhance existing protocols, and investigate the role of optical amplifiers for the task. Finally, we make a first step towards a fully non-Gaussian CVQKD scheme by proposing, for the first time, the adoption of an optimized state-discrimination receiver, commonly adopted for quantum decision theory, within the context of CVQKD, obtaining a genuine quantum enhancement over conventional protocols.
An improved continuous variable quantum key distribution (CVQKD) approach based on a heralded hybrid linear amplifier (HLA) is proposed in this study, which includes an ideal deterministic linear amplifier and a probabilistic noiseless linear amplifier. The CVQKD, which is based on an amplifier, enhances the signal-to-noise ratio and provides for fine control between high gain and strong noise reduction. We focus on the impact of two types of optical amplifiers on system performance: phase sensitive amplifiers (PSA) and phase insensitive amplifiers (PIA). The results indicate that employing amplifiers, local local oscillation-based CVQKD systems can enhance key rates and communication distances. In addition, the PIA-based CVQKD system has a broader application than the PSA-based system.