Gaussian-modulated Coherent States Research Articles

Experimental realization of free-space continuous-variable quantum key distribution based on fiber Sagnac interferometer.

The Gaussian-modulated coherent state (GMCS) is a well-known continuous-variable quantum key distribution (CV-QKD) protocol that is robust to incoherent background noise and can effectively suppress ambient light in free space. However, it is difficult to implement this protocol in free space using existing polarization coding schemes. In this Letter, we propose a polarization coding structure based on a self-compensating fiber Sagnac interferometer, which can reduce the required modulation voltage by two orders of magnitude and achieve fast and arbitrary polarization modulation, and experimentally demonstrate polarization coding-based GMCS CV-QKD for, it is believed, the first time. The proposed polarization modulation structure, which uses off-the-shelf fiber components, is compact, simple, and suitable for mobile terminals, such as flying lifts.

Continuous-variable quantum key distribution with time-division dual-quadrature homodyne detection.

We propose a novel heterodyne detection scheme for continuous-variable quantum key distribution (CVQKD), which measures both quadrature components of a quantum signal encoded in optical phase space. The proposed method uses time division to achieve identical performance to conventional heterodyne detection with only a single homodyne detection system. Our method also uses a Faraday-Michelson interferometer to make it independent of polarization drift and eliminate the need for dynamic polarization control. Our method is experimentally demonstrated using the Gaussian-modulated coherent-states (GMCS) protocol over a 20.06 km optical fiber channel, achieving an expected secret key rate of up to 0.187 Mbps.

Experimental Demonstration of LLO Continuous-Variable Quantum Key Distribution With Polarization Loss Compensation

The compensation process for the state of polarization (SOP) from quantum signal plays an important role in the practical implementation of continuous-variable quantum key distribution (CV-QKD). In contrast to the previous scheme using an expensive digital dynamic polarization controller, we choose a cheaper manual polarization controller interfaced with a digital algorithm based on Kalman filter to achieve compensation of the polarization loss under the condition that the SOP of the fiber is relatively stable. This paper also enumerates the details of other digital signal processing method to achieve final secret key rate. And a pilot-sequential Gaussian modulated coherent state (GMCS) continuous-variable quantum key distribution system with a local local oscillator (LLO) is experimentally implemented based on the analysis of excess noise. Finally, the experimental results show that the method of polarization loss compensation takes advantages in maintaining the stability of the final secret key rate. And a secret key rate of 110 kbps is achieved within 20 km optical fiber (with 4 dB loss) under the finite-size block of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$1 \times {10^{6}}$</tex-math></inline-formula> during a more extended time in the laboratory.

Sub-Mbps key-rate continuous-variable quantum key distribution with local local oscillator over 100-km fiber.

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.

Small-form-factor Gaussian-modulated coherent-state transmitter for CV-QKD using a gain-switched DFB laser.

We report a directly modulated distributed feedback laser operating in gain-switching mode for preparing the coherent states required for the Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) protocol. The proposed single-component quantum transmitter design eliminates the need for external modulators, decreasing the complexity of GMCS CV-QKD systems. The experimental results demonstrate a potential asymptotic secret key rate value of 2.63 Mbps over an 11-km fiber link, making the directly modulated GMCS transmitter particularly suitable for metropolitan optical networks where compactness, robustness, and low cost are key desirable features.

Practical continuous-variable quantum key distribution with composable security

A quantum key distribution (QKD) system must fulfill the requirement of universal composability to ensure that any cryptographic application (using the QKD system) is also secure. Furthermore, the theoretical proof responsible for security analysis and key generation should cater to the number N of the distributed quantum states being finite in practice. Continuous-variable (CV) QKD based on coherent states, despite being a suitable candidate for integration in the telecom infrastructure, has so far been unable to demonstrate composability as existing proofs require a rather large N for successful key generation. Here we report a Gaussian-modulated coherent state CVQKD system that is able to overcome these challenges and can generate composable keys secure against collective attacks with N ≈ 2 × 108 coherent states. With this advance, possible due to improvements to the security proof and a fast, yet low-noise and highly stable system operation, CVQKD implementations take a significant step towards their discrete-variable counterparts in practicality, performance, and security.

Experimental continuous-variable quantum key distribution using a thermal source

Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CVQKD) protocol can allow authenticated users to share secret key with unconditional security. So far, all previous experimental implementations of GMCS CVQKD schemes are based on active modulations, i.e. amplitude and phase modulators and quantum random number generator (QRNG) are required. However, high-speed modulation with high extinction ratio and stability is challenging, which is extremely remarkable in chip-scale silicon photonic realization. While the passive-state-preparation (PSP) CVQKD scheme, which explores the intrinsic field fluctuations of a thermal source, avoids the uses of active modulations and QRNG. In this paper, we experimentally realize the intact PSP CVQKD through a realistic optical fiber channel using off-the-shelf amplified spontaneous emission source. In particular, specially designed frame synchronization method is used to build the correlation between the data measured from the two legitimate parties, and excess noise are synthetically controlled to generate secure secret keys at the metro-area distances when considering the practical and non-negligible finite-size effects under collective Gaussian attacks. Due to the avoidance of modulators and QRNG, the passive state encoding scheme provides a promising direction of applicable high-speed, chip-based and even sunlight-based CVQKD with less cost and complexity.

Performance improvement of unidimensional continuous-variable quantum key distribution using zero-photon quantum catalysis

Compared with symmetric Gaussian-modulated coherent state protocol, the unidimensional continuous-variable quantum key distribution (UCVQKD) only modulates one of the quadratures in phase space of coherent state, thereby simplifying its implementation. Although UCVQKD does reduce the system’s complexity, its performance is reduced. In this work, we suggest an improved approach for UCVQKD using zero-photon quantum catalysis (ZPQC) technology. By taking advantage of this non-Gaussian operation, both secret key rate and maximal transmission distance of UCVQKD can be enhanced. Moreover, compared with another well-studied non-Gaussian operation, i.e., photon subtraction, ZPQC has higher success possibility, so that it would be beneficial for improving the amount of information acquired by legitimate users. Numerical simulation shows that the performance of UCVQKD can be improved by properly applying ZPQC. In particular, we find out that the performance of ZPQC-based UCVQKD outperforms that of photon subtraction-based UCVQKD, thereby providing an alternative way to better improve UCVQKD system. Furthermore, by taking finite-size effect into account, we derive more practical secure bound of ZPQC-based UCVQKD.

Continuous-variable measurement-device-independent quantum key distribution with source-intensity errors

Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) is immune to all detector side channel attacks, however its security requires trusted sources. We investigate the effects of source intensity errors, the most crucial source error, on the security of CV-MDI-QKD protocol with Gaussian-modulated coherent states. We establish a general source intensity errors model and derive the secret key rate based on different assumptions on the abilities of legal parties Alice and Bob. To avoid the adverse effects of the sources' intensity errors on CV-MDI-QKD, we present different data-processing schemes. We also assess the security of the protocol against collective Gaussian attacks in the finite-size scenario with composable security. Taking source intensity errors into consideration, we achieve improved security compared to previous demonstrations. Our results will provide a useful reference for practical implementations of CV-MDI-QKD.

Performance improvement of plug-and-play dual-phase-modulated continuous-variable quantum key distribution with quantum catalysis

Continuous-variable quantum key distribution based on plug-and-play dual-phase-modulated coherent-states (DPMCS) protocol has been proved to be equivalent to the one-way Gaussian-modulated coherent-states protocol, but it is not just limited to this. This protocol can effectively against the LO-aimed attacks and maintain the system robust. However, the maximum transmission distance of the protocol is restricted due to its large excess noise. In this paper, we enhance the plug-and-play DPMCS protocol using quantum catalysis operation, which can be implemented by the existing technologies. To further highlight the advantage of the implementation of quantum catalysis operation, we make performance comparison not only between the proposed protocol and the original scheme but also the single-photon subtraction-based (SPS) plug-and-play DPMCS protocol. Security analysis shows that the proposed protocol can extend the maximum transmission distance up to hundreds of kilometers even under the effect of the imperfect source noise and show more excellent performance than the SPS-based plug-and-play DPMCS protocol. Furthermore, we also take the finite-size effect into consideration and thus achieve more practical results than those obtained in the asymptotic limit.

Experimental Passive-State Preparation for Continuous-Variable Quantum Communications

In the Gaussian-modulated coherent state quantum key distribution (QKD) protocol, the sender first generates Gaussian distributed random numbers and then encodes them on weak laser pulses actively by performing amplitude and phase modulations. Recently, an equivalent passive QKD scheme was proposed by exploring the intrinsic field fluctuations of a thermal source [B. Qi, P. G. Evans, and W. P. Grice, Phys. Rev. A 97, 012317 (2018)]. This passive QKD scheme is especially appealing for chip-scale implementation since no active modulations are required. In this paper, we conduct an experimental study of the passively encoded QKD scheme using an off-the-shelf amplified spontaneous emission source operated in continuous-wave mode. Our results show that the excess noise introduced by the passive state preparation scheme can be effectively suppressed by applying optical attenuation and secure key could be generated over metro-area distances.

Performance of continuous variable quantum key distribution system at different detector bandwidth

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.

Imperfect basis choice in continuous-variable quantum key distribution

In the Gaussian-modulated coherent states (GMCS) quantum key distribution (QKD), basis choice is a necessary procedure if homodyne detector is used. However, finite bandwidth of the digital-to-analog convertor (DAC) at the receiver’s side may lead to the imperfection of the basis choice, namely, maybe Bob can not exactly modulate 0 or on the phase modulator to implement the homodyne detection.We investigate the GMCS QKD scheme with imperfect basis choice under realistic conditions of quantum channel and detector.We show that the imperfection causes a misestimate of the transmittance and the excess noise, the secret key rate and the security of the system are dramatically decreased consequently. To achieve a reliable quantum key distribution, a security bound to the noise induced by the imperfect basis choice is derived for reverse reconciliation and homodyne detector. Besides, we propose and demonstrate a countermeasure against the noise due to imperfect basis choice.

Improving Continuous Variable Quantum Secret Sharing with Weak Coherent States

Quantum secret sharing (QSS) can usually realize unconditional security with entanglement of quantum systems. While the usual security proof has been established in theoretics, how to defend against the tolerable channel loss in practices is still a challenge. The traditional ( t , n ) threshold schemes are equipped in situation where all participants have equal ability to handle the secret. Here we propose an improved ( t , n ) threshold continuous variable (CV) QSS scheme using weak coherent states transmitting in a chaining channel. In this scheme, one participant prepares for a Gaussian-modulated coherent state (GMCS) transmitted to other participants subsequently. The remaining participants insert independent GMCS prepared locally into the circulating optical modes. The dealer measures the phase and the amplitude quadratures by using double homodyne detectors, and distributes the secret to all participants respectively. Special t out of n participants could recover the original secret using the Lagrange interpolation and their encoded random numbers. Security analysis shows that it could satisfy the secret sharing constraint which requires the legal participants to recover message in a large group. This scheme is more robust against background noise due to the employment of double homodyne detection, which relies on standard apparatuses, such as amplitude and phase modulators, in favor of its potential practical implementations.

Unidimensional Continuous-Variable Quantum Key Distribution with Untrusted Detection under Realistic Conditions

A unidimensional continuous-variable quantum key distribution protocol with untrusted detection is proposed, where the two legitimate partners send unidimensional modulated or Gaussian-modulated coherent states to an untrusted third party, i.e., Charlie, to realize the measurement. Compared with the Gaussian-modulated coherent-state protocols, the unidimensional modulated protocols take the advantage of easy modulation, low cost, and only a small number of random numbers required. Security analysis shows that the proposed protocol cannot just defend all detectors side channels, but also achieve great performance under certain conditions. Specifically, three cases are discussed in detail, including using unidimensional modulated coherent states in Alice’s side, in Bob’s side, and in both sides under realistic conditions, respectively. Under the three conditions, we derive the expressions of the secret key rate and give the optimal gain parameters. It is found that the optimal performance of the protocol is achieved by using unidimensional modulated coherent states in both Alice’s and Bob’s side. The resulting protocol shows the potential for long-distance secure communication using the unidimensional quantum key distribution protocol with simple modulation method and untrusted detection under realistic conditions.

An integrated silicon photonic chip platform for continuous-variable quantum key distribution

Quantum key distribution (QKD) is a quantum communication technology that promises unconditional communication security. High-performance and cost-effective QKD systems are essential for the establishment of quantum communication networks1–3. By integrating all the optical components (except the laser source) on a silicon photonic chip, we have realized a stable, miniaturized and low-cost system for continuous-variable QKD (CV-QKD) that is compatible with the existing fibre optical communication infrastructure4. Here, the integrated silicon photonic chip is demonstrated for CV-QKD. It implements the widely studied Gaussian-modulated coherent state protocol that encodes continuous distributed information on the quadrature of laser light5,6. Our proof-of-principle chip-based CV-QKD system is capable of producing a secret key rate of 0.14 kbps (under collective attack) over a simulated distance of 100 km in fibre, offering new possibilities for low-cost, scalable and portable quantum networks. A sender and a receiver for continuous-variable quantum key distribution are packed onto separate silicon photonic chips. By using an external 1,550-nm laser, a secret key rate of 0.14 kbps is transmitted over a simulated distance of 100 km in fibre.

Practical security of continuous-variable quantum key distribution with reduced optical attenuation

In a practical CVQKD system, the optical attenuator can adjust the Gaussian-modulated coherent states and the local oscillator signal to an optimal value for guaranteeing the security of the system and optimizing the performance of the system. However, the performance of the optical attenuator may deteriorate due to the intentional and unintentional damage of the device. In this paper, we investigate the practical security of a CVQKD system with reduced optical attenuation. We find that the secret key rate of the system may be overestimated based on the investigation of parameter estimation under the effects of reduced optical attenuation. This opens a security loophole for Eve to successfully perform an intercept-resend attack in a practical CVQKD system. To close this loophole, we add an optical fuse at Alice's output port and design a scheme to monitor the level of optical attenuation in real time, which can make the secret key rate of the system evaluated precisely. The analysis shows that these countermeasures can effectively resist this potential attack.

Plug-and-play dual-phase-modulated continuous-variable quantum key distribution with photon subtraction

Plug-and-play dual-phase-modulated continuous-variable quantum key distribution (CVQKD) protocol can effectively solve the security loopholes associated with transmitting local oscillator (LO). However, this protocol has larger excess noise compared with one-way Gaussian-modulated coherent-states scheme, which limits the maximal transmission distance to a certain degree. In this paper, we show a reliable solution for this problem by employing non-Gaussian operation, especially, photon subtraction operation, which provides a way to improve the performance of plug-and-play dual-phase-modulated CVQKD protocol. The photon subtraction operation shows experimental feasibility in the plug-andplay configuration since it can be implemented under current technology. Security results indicate that the photon subtraction operation can evidently enhance the maximal transmission distance of the plug-and-play dual-phase-modulated CVQKD protocol, which effectively makes up the drawback of the original one. Furthermore, we achieve the tighter bound of the transmission distance by considering the finite-size effect, which is more practical compared with that achieved in the asymptotic limit.

Performance Analysis of Continuous-Variable Quantum Key Distribution with Multi-Core Fiber

Performance analysis of continuous-variable quantum key distribution (CVQKD) has been one of the focuses of quantum communications. In this paper, we propose an approach to enhancing the secret rate of CVQKD with the multi-core fiber (MCF) system that transmits multiple spatial modes simultaneously. The excess noise contributed by the inter-core crosstalk between cores can be effectively suppressed by quantum channel wavelength management, leading to the performance improvement of the MCF-based CVQKD system. In the security analysis, we perform numerical simulations for the Gaussian-modulated coherent state CVQKD protocol, considering simultaneously the extra insert loss of fan-in/fan-out (FIFO), which is the extra optical device that should be used at the input and the output of the fiber. Simulation results show that the performance of the one-way and two-way protocols for each core are slightly degraded because of the insert loss of the FIFO, but the total secret key rate can be increased, whereas the performance of the measurement-device-independent CVQKD protocol will be degraded due to the effect of the insert loss of the FIFO. These results may provide theoretical foundation for the space-division multiplexing CVQKD system.

Continuous-variable quantum key distribution based on continuous random basis choice**Project supported by the National Natural Science Foundation of China (Grant Nos. 61332019, 61671287, and 61631014), Northwest University Doctorate Dissertation of Excellence Funds, China (Grant No. YYB17022), and the National Key Research and Development Program, China (Grant No. 2016YFA0302600).

Gaussian-modulated coherent state quantum key distribution is gradually moving towards practical application. Generally, the involved scheme is based on the binary random basis choice. To improve the performance and security, we present a scheme based on a continuous random basis choice. The results show that our scheme obviously improves the performance, such as the secure communication distance. Our scheme avoids comparing the measurement basis and discarding the key bits, and it can be easily implemented with current technology. Moreover, the imperfection of the basis choice can be well removed by the known phase compensation algorithm.