Discrete-variable Quantum Key Distribution Research Articles

Discrete-variable quantum key distribution services hosted in legacy passive optical networks [Invited

Fiber-based quantum key distribution (QKD) systems are mature and commercialized, but their integration into existing optical networks is crucial for their widespread use, in particular in passive optical networks (PONs) if end-to-end quantum-secured communications are to be addressed. While discrete-variable QKD coexistence with classical channels is well-studied in point-to-point links, its performance in point-to-multipoint topologies like PONs has received less attention. We thus developed a numerical tool to estimate quantum-available bandwidth and maximum link lengths for QKD systems in single-fiber PON architectures in coexistence with GPON, XG-PON, NG-PON2, and HS-PON standards. The QKD channel performance is obtained by setting thresholds on the quantum bit error rate and the secret key rate, ultimately limited by spontaneous Raman scattering noise and high optical distribution network losses. We perform a comparison between the performance obtained assuming the asymptotic infinite-key generation rate or taking into account actual implementations in the finite-key regime. We evidence that proper design rules can be obtained as a function of both classical and quantum system parameters to support end-to-end quantum security services in existing optical networks.

Robustness of entanglement-based discrete- and continuous-variable quantum key distribution against channel noise

Discrete-variable (DV) and continuous-variable (CV) schemes constitute the two major families of quantum key distribution (QKD) protocols. Unfortunately, since the setup elements required by these schemes are quite different, making a fair comparison of their potential performance in particular applications is often troublesome, limiting the experimenters’ capability to choose an optimal solution. In this work we perform a general comparison of the major entanglement-based DV and CV QKD protocols in terms of their resistance to the channel noise, with the otherwise perfect setup, showing the definite superiority of the DV family. We analytically derive fundamental bounds on the tolerable channel noise and attenuation for entanglement-based CV QKD protocols. We also investigate the influence of DV QKD setup imperfections on the obtained results in order to determine benchmarks for the parameters of realistic photon sources and detectors, allowing the realistic DV protocols to outperform even the ideal CV QKD analogs. Our results indicate the realistic advantage of DV entanglement-based schemes over their CV counterparts and suggests the practical efforts for maximizing this advantage.

Homodyne-detection-based discrete-variable quantum key distribution with a heralded single-photon source

Discrete-variable quantum key distribution (DV-QKD) has recently been implemented using a homodyne detection system, and a notable secret key rate can be achieved by employing an ideal single-photon source. However, most QKD implementations employ practical light sources, including a phase-randomized weak coherent source and a heralded single-photon source, which occasionally produce multiphotons and are vulnerable to photon-number-splitting (PNS) attacks. In this work, we propose a three-decoy-state method using a heralded single-photon source for homodyne-detection-based DV-QKD, thus making it immune to PNS attacks with current technology. Our simulation results demonstrate that our proposed protocol can achieve high-speed and secure key distribution over metropolitan distances. Our work paves a cost-effective path to realize DV-QKD and further incorporate it into classical telecommunication networks.

Coexistence of 1 Tbps classical optical communication and quantum key distribution over a 100.96 km few-mode fiber.

The integration of quantum key distribution (QKD) and classical optical communication has attracted widespread attention. In this Letter, we experimentally demonstrate a real-time co-propagation of 1 Tbps for 10 classical channels with one discrete-variable QKD channel in the weakly coupled few-mode fiber (FMF). Based on the selection of optimal device parameters and wavelength assignment of classical channels, as well as the optimization of equipment performance, a secure key rate of as high as 2.7 kbps of coexistence transmission of QKD and classical optical communication can be achieved using a 100.96 km weakly coupled FMF. Therefore, this study is a step toward realizing long-distance quantum-classical coexistence transmission.

Refined finite-size analysis of binary-modulation continuous-variable quantum key distribution

Recent studies showed the finite-size security of binary-modulation CV-QKD protocols against general attacks. However, they gave poor key-rate scaling against transmission distance. Here, we extend the security proof based on complementarity, which is used in the discrete-variable QKD, to the previously developed binary-modulation CV-QKD protocols with the reverse reconciliation under the finite-size regime and obtain large improvements in the key rates. Notably, the key rate in the asymptotic limit scales linearly against the attenuation rate, which is known to be optimal scaling but is not achieved in previous finite-size analyses. This refined security approach may offer full-fledged security proofs for other discrete-modulation CV-QKD protocols.

Optical transmitter for time-bin encoding quantum key distribution

We introduce an electro-optical arrangement that can produce time-bin encoded symbols with the decoy state method over a standard optical fiber in the C-band telecom window. The device consists of a specifically designed pulse pattern generator for pulse production and a field-programmable gate array that controls timing and synchronization. The electrical pulse output drives a sequence of intensity modulators acting on a continuous laser that deliver bursts of weak optical pulse pairs of discrete intensity values. Such a transmitter allows for the generation of all the quantum states needed to implement a discrete variable quantum key distribution (QKD) protocol over a single-mode fiber channel. Symbols are structured in bursts; the minimum relative delay between pulses is 1.25 ns, and the maximum symbol rate within a burst is 200 MHz. We tested the transmitter on simulated optical channels of 7 dB and 14 dB loss, obtaining maximum extractable secure key rates of 3.0 kb/s and 0.57 kb/s, respectively. Time-bin-state parameters such as the symbol rate, pulse separation, and intensity ratio between the signal and decoy states can be easily accessed and changed, allowing the transmitter to adapt to different experimental conditions and contributing to the standardization of QKD implementations.

On the Security of Offloading Post-Processing for Quantum Key Distribution.

Quantum key distribution (QKD) has been researched for almost four decades and is currently making its way to commercial applications. However, deployment of the technology at scale is challenging because of the very particular nature of QKD and its physical limitations. Among other issues, QKD is computationally intensive in the post-processing phase, and devices are therefore complex and power hungry, which leads to problems in certain application scenarios. In this work, we study the possibility to offload computationally intensive parts in the QKD post-processing stack in a secure way to untrusted hardware. We show how error correction can be securely offloaded for discrete-variable QKD to a single untrusted server and that the same method cannot be used for long-distance continuous-variable QKD. Furthermore, we analyze possibilities for multi-server protocols to be used for error correction and privacy amplification. Even in cases where it is not possible to offload to an external server, being able to delegate computation to untrusted hardware components on the device itself could improve the cost and certification effort for device manufacturers.

Simple and Rigorous Proof Method for the Security of Practical Quantum Key Distribution in the Single-Qubit Regime Using Mismatched Basis Measurements

Quantum key distribution (QKD) protocols aim at allowing two parties to generate a secret shared key. While many QKD protocols have been proven unconditionally secure in theory, practical security analyses of experimental QKD implementations typically do not take into account all possible loopholes, and practical devices are still not fully characterized for obtaining tight and realistic key rates. We present a simple method of computing secure key rates for any practical implementation of discrete-variable QKD (which can also apply to measurement-device-independent QKD), initially in the single-qubit lossless regime, and we rigorously prove its unconditional security against any possible attack. We hope our method becomes one of the standard tools used for analysing, benchmarking, and standardizing all practical realizations of QKD.

Regression-decision-tree based parameter optimization of measurement-device-independent quantum key distribution

The parameter configuration of quantum key distribution (QKD) has a great effect on the communication effect, and in the practical application of the QKD network in the future, it is necessary to quickly realize the parameter configuration optimization of the asymmetric channel measurement-device-independent QKD according to the communication state, so as to ensure the good communication effect of the mobile users, which is an inevitable requirement for real-time quantum communication. Aiming at the problem that the traditional QKD parameter optimization configuration scheme cannot guarantee real-time, in this paper we propose to apply the supervised machine learning algorithm to the QKD parameter optimization configuration, and predict the optimal parameters of TF-QKD and MDI-QKD under different conditions through the machine learning model. First, we delineate the range of system parameters and evenly spaced (linear or logarithmic) values through experimental experience, and then use the traditional local search algorithm (LSA) to obtain the optimal parameters and take them as the optimal parameters in this work. Finally, we train various machine learning models based on the above data and compare their performances. We compare the supervised regression learning models such as neural network, K-nearest neighbors, random forest, gradient tree boosting and classification and regression tree (CART), and the results show that the CART decision tree model has the best performance in the regression evaluation index, and the average value of the key rate (of the prediction parameters) and the optimal key rate ratio is about 0.995, which can meet the communication needs in the actual environment. At the same time, the CART decision tree model shows good environmental robustness in the residual analysis of asymmetric QKD protocol. In addition, compared with the traditional scheme, the new scheme based on CART decision tree greatly improves the real-time performance of computing, shortening the single prediction time of the optimal parameters of different environments to the microsecond level, which well meets the real-time communication needs of the communicator in the movable state. This work mainly focuses on the parameter optimization of discrete variable QKD (DV-QKD). In recent years, the continuous variable QKD (CV-QKD) has developed also rapidly. At the end of the paper, we briefly introduce academic attempts of applying machine learning to the parameter optimization of CV-QKD system, and discuss the applicability of the scheme in CV-QKD system.

Fully integrated four-channel wavelength-division multiplexed QKD receiver

Quantum key distribution (QKD) enables secure communication even in the presence of advanced quantum computers. However, scaling up discrete-variable QKD to high key rates remains a challenge due to the lossy nature of quantum communication channels and the use of weak coherent states. Photonic integration and massive parallelization are crucial steps toward the goal of high-throughput secret-key distribution. We present a fully integrated photonic chip on silicon nitride featuring a four-channel wavelength-division demultiplexed QKD receiver circuit including state-of-the-art waveguide-integrated superconducting nanowire single-photon detectors (SNSPDs). With a proof-of-principle setup operated at a clock rate of 3.35 GHz, we achieve a total secret-key rate of up to 12.17 Mbit/s at 10 dB channel attenuation with low detector-induced error rates. The QKD receiver architecture is massively scalable and constitutes a foundation for high-rate many-channel QKD transmission.

Dynamic DV-QKD Networking in Trusted-Node-Free Software-Defined Optical Networks

We demonstrate for the first time a four-node trusted-node-free metro network configuration with dynamic discrete-variable quantum key distribution DV-QKD networking capabilities across four optical network nodes. The network allows the dynamic deployment of any QKD link between two nodes of the network, while a QKD-aware centralised software-defined networking (SDN) controller is utilised to provide dynamicity in switching and rerouting. The feasibility of coexisting a quantum channel with carrier-grade classical optical channels where both the quantum and classical channels are in the C-band over field-deployed metropolitan networks and laboratory-based fibres (<10 km) is experimentally explored in terms of achievable quantum bit error rate, secret key rate as well as classical signal bit error rate. Moreover, coexistence analysis over multi-hops configuration using different switching scenarios is also presented. The secret key rate dropped 43% when coexisting one classical channel with 150 GHz spacing from the quantum channel for multiple links. This is due to the noise leakage from the Raman scattering into the 100 GHz bandwidth of the internal filter of the Bob DV-QKD unit. When coexisting four classical channels with 150 GHz spacing between quantum and the nearest classical channel, the quantum channel deteriorates faster due to the combination of Raman noise, other nonlinearities and high aggregated launch power causing the QBER value to exceed the threshold of 6% leading the SKR to reach a value of zero bps at a launch power of 7 dB per channel. Furthermore, the coexistence of a quantum channel and six classical channels through a field-deployed fibre test network is examined.

Experimental study of secure quantum key distribution with source and detection imperfections

The quantum key distribution (QKD), guaranteed by the principle of quantum physics, is a promising solution for future secure information and communication technology. However, device imperfections compromise the security of real-life QKD systems, restricting the wide deployment of QKD. This study reports a decoy-state BB84 QKD experiment that considers both source and detection imperfections. In particular, we achieved a rigorous finite-key security bound over fiber links of up to 75 km by applying a systematic performance analysis. Furthermore, our study considers more device imperfections than most previous experiments, and the proposed theory can be extended to other discrete-variable QKD systems. These features constitute a crucial step toward securing QKD with imperfect practical devices.

Polarization based discrete variables quantum key distribution via conjugated homodyne detection

Optical homodyne detection is widely adopted in continuous-variable quantum key distribution for high-rate field measurement quadratures. Besides that, those detection schemes have been being implemented for single-photon statistics characterization in the field of quantum tomography. In this work, we propose a discrete-variable quantum key distribution (DV-QKD) implementation that combines the use of phase modulators for high-speed state of polarization (SOP) generation, with a conjugate homodyne detection scheme which enables the deployment of high speed QKD systems. The channel discretization relies on the application of a detection threshold that allows to map the measured voltages as a click or no-click. Our scheme relies also on the use of a time-multiplexed pilot tone—quantum signal architecture which enables the use of a Bob locally generated local oscillator and opens the door to an effective polarization drift compensation scheme. Besides that, our results shows that for higher detection threshold values we obtain a very low quantum bit error rate (QBER) on the sifted key. Nevertheless, due to huge number of discarded qubits the obtained secure key length abruptly decreases. From our results, we observe that optimizing the detection threshold and considering a system operating at 500 MHz symbol generation clock, a secure key rate of approximately 46.9 Mbps, with a sifted QBER of 1.5% over 40 km of optical fiber. This considering the error correction and privacy amplification steps necessary to obtain a final secure key.

Networking Feasibility of Quantum Key Distribution Constellation Networks.

Quantum key distribution constellation is the key to achieve global quantum networking. However, the networking feasibility of quantum constellation that combines satellite-to-ground accesses selection and inter-satellite routing is faced with a lack of research. In this paper, satellite-to-ground accesses selection is modeled as problems to find the longest paths in directed acyclic graphs. The inter-satellite routing is interpreted as problems to find a maximum flow in graph theory. As far as we know, the above problems are initially understood from the perspective of graph theory. Corresponding algorithms to solve the problems are provided. Although the classical discrete variable quantum key distribution protocol, i.e., BB84 protocol, is applied in simulation, the methods proposed in our paper can also be used to solve other secure key distributions. The simulation results of a low-Earth-orbit constellation scenario show that the Sun is the leading factor in restricting the networking. Due to the solar influence, inter-planar links block the network periodically and, thus, the inter-continental delivery of keys is restricted significantly.

Sifting scheme for continuous-variable quantum key distribution with short samples

Preventing the secret key from being stolen is an important issue in practical quantum key distribution systems. In the sifting step, the legitimate parties discard the useless portion of the raw data to form the sifted key. This step is executed at high speed to support the high repetition frequency of the systems without guaranteeing the security of the raw data. In practical systems, useless data contain abnormal data and the key measured by the legitimate party on different bases. Here we propose a sifting scheme based on machine learning that can monitor anomaly quantum signal disturbances in practical continuous-variable quantum key distribution systems. It randomly samples small amounts of data from the data block and uses short samples to preliminarily sift the abnormal one. The results show that the model can quickly distinguish normal communication from most common attacks with the cost of a small part of the raw keys and improve system performance under attacks. In principle, the model can also be generalized and applied to discrete-variable quantum key distribution systems and further enhance the security of quantum key distribution.

Discrete-variable quantum key distribution with homodyne detection

Most quantum key distribution (QKD) protocols can be classified as either a discrete-variable (DV) protocol or continuous-variable (CV) protocol, based on how classical information is being encoded. We propose a protocol that combines the best of both worlds – the simplicity of quantum state preparation in DV-QKD together with the cost-effective and high-bandwidth of homodyne detectors used in CV-QKD. Our proposed protocol has two highly practical features: (1) it does not require the honest parties to share the same reference phase (as required in CV-QKD) and (2) the selection of decoding basis can be performed after measurement. We also prove the security of the proposed protocol in the asymptotic limit under the assumption of collective attacks. Our simulation suggests that the protocol is suitable for secure and high-speed practical key distribution over metropolitan distances.

Quantum key distribution integrating with ultra-high-power classical optical communications based on ultra-low-loss fiber.

The demand for the integration of quantum key distribution (QKD) and classical optical communication in the same optical fiber medium greatly increases as fiber resources and the flexibility of practical applications are taken into consideration. To satisfy the needs of the mass deployment of ultra-high power required for classical optical networks integrating QKD, we implement the discrete variable quantum key distribution (DV-QKD) under up to 25 dBm launch power from classical channels over 75 km on an ultra-low-loss (ULL) fiber by combining a finite-key security analysis method with the noise model of classical signals. To the best of our knowledge, this is the highest power launched by classical signals on the coexistence of DV-QKD and classical communication. The results exhibit the feasibility and tolerance of our QKD system for use in ultra-high-power classical communications.

Heterogeneously integrated, superconducting silicon-photonic platform for measurement-device-independent quantum key distribution

Integrated photonics provides a route to both miniaturization of quantum key distribution (QKD) devices and enhancing their performance. A key element for achieving discrete-variable QKD is a single-photon detector. It is highly desirable to integrate detectors onto a photonic chip to enable the realization of practical and scalable quantum networks. We realize a heterogeneously integrated, superconducting silicon-photonic chip. Harnessing the unique high-speed feature of our optical waveguide-integrated superconducting detector, we perform the first optimal Bell-state measurement (BSM) of time-bin encoded qubits generated from two independent lasers. The optimal BSM enables an increased key rate of measurement-device-independent QKD (MDI-QKD), which is immune to all attacks against the detection system and hence provides the basis for a QKD network with untrusted relays. Together with the time-multiplexed technique, we have enhanced the sifted key rate by almost one order of magnitude. With a 125-MHz clock rate, we obtain a secure key rate of 6.166 kbps over 24.0 dB loss, which is comparable to the state-of-the-art MDI-QKD experimental results with a GHz clock rate. Combined with integrated QKD transmitters, a scalable, chip-based, and cost-effective QKD network should become realizable in the near future.

Simple security proofs for continuous variable quantum key distribution with intensity fluctuating sources

Despite tremendous theoretical and experimental progress in continuous variable (CV) quantum key distribution (QKD), the security has not been rigorously established for most current continuous variable quantum key distribution systems that have imperfections. Among these imperfections, intensity fluctuation is one of the principal problems affecting security. In this paper, we provide simple security proofs for continuous variable quantum key distribution systems with intensity fluctuating sources. Specifically, depending on device assumptions in the source, the imperfect systems are divided into two general cases for security proofs. In the most conservative case, we prove the security based on the tagging idea, which is a main technique for the security proof of discrete variable quantum key distribution. Our proofs are simple to implement without any hardware adjustment for current continuous variable quantum key distribution systems. Also, we show that our proofs are able to provide secure secret keys in the finite-size scenario.

The limits of multiplexing quantum and classical channels: Case study of a 2.5 GHz discrete variable quantum key distribution system

Network integration of quantum key distribution is crucial for its future widespread deployment due to the high cost of using optical fibers dedicated for the quantum channel only. We studied the performance of a system running a simplified BB84 protocol at 2.5 GHz repetition rate, operating in the original wavelength band, the short O-band, when multiplexed with communication channels in the conventional wavelength band, and the short C-band. Our system could successfully generate secret keys over a single-mode fiber with a length of 95.5 km and with co-propagating classical signals at a launch power of 8.9 dBm. Furthermore, we discuss the performance of an ideal system under the same conditions, showing the limits of what is possible with a discrete variable system in the O-band. We also considered a short and lossy link with 51 km optical fiber resembling a real link in a metropolitan area network. In this scenario, we could exchange a secret key with a launch power up to 16.7 dBm in the classical channels.