Final Key Rate Research Articles

Physical-layer key distribution using synchronous complex dynamics of DBR semiconductor lasers

Common-signal-induced synchronization of semiconductor lasers with optical feedback inspired a promising physical-layer key distribution with information-theoretic security and potential in high rate. A significant challenge is the requirement to shorten the synchronization recovery time for increasing the key rate without sacrificing the operation parameter space for security. Here, open-loop synchronization of wavelength-tunable multi-section distributed Bragg reflector lasers is proposed as a solution for physical-layer key distribution. Experiments show that the synchronization is sensitive to two operation parameters, i.e., currents of grating section and phase section. Furthermore, fast wavelength-shift keying synchronization can be achieved by direct modulation on one of the two currents. The synchronization recovery time is shortened by one order of magnitude compared to close-loop synchronization. An experimental implementation is demonstrated with a final key rate of 5.98 Mbit/s over 160 km optical fiber distance. It is thus believed that fast-tunable multi-section semiconductor lasers open a new avenue for a high-rate physical-layer key distribution using laser synchronization.

A 300 km fiber channel mapping using neural networks for Gb/s physical-layer key distribution.

Physical-layer secure key distribution (PLSKD) generally acquires highly correlated entropy sources via bidirectional transmission to share the channel reciprocity. For long-haul fiber links, the non-negligible backscattering noise (BSN) and the challenge of bidirectional optical amplification degrade the key generation performances. Since the channel reciprocity can be precisely mapped using neural networks (NNs), unidirectional PLSKD provides a feasible PLSKD for longer fiber links. Here, a final error-free key generation rate (KGR) in unidirectional PLSKD of 3.07 Gb/s is demonstrated over a 300 km fiber link using NNs. Moreover, the channel mapping is analyzed in terms of fiber distance, chromatic dispersion, the nonlinearity of random source, and BSN.

Physical-layer key distribution based on commonly-driven laser synchronization with random modulation of drive light.

We propose and experimentally demonstrate a physical-layer key distribution scheme using commonly-driven laser synchronization with random modulation of drive light. Two parameter-matched semiconductor lasers injected by a common complex drive light are used as entropy sources for legitimate users. Legitimate users generate their own random signal by randomly time-division multiplexing of two random sequences with a certain duration according to individual control codes, and then independently modulate the drive light. Laser synchronization is achieved during time slots when the modulation sequences of two users are identical, and thus provide highly correlated randomness for extracting random numbers as shared keys. Experimental results show that the random modulation of the drive light reduces the correlation between the drive light and laser outputs. In addition, laser synchronization is sensitive to the modulation delay and then the latter can be used as an additional hardware parameter. These mean that security is enhanced. In addition, the proposed method has a short laser synchronization recovery time of lower than 1.1 ns, meaning a high rate of key distribution. The upper limit of final key rate of 2.55 Gb/s with a criterion of bit error rate of 1.68 × 10-3 is achieved in experiments. Our results provide a promising candidate for protecting the security of optical fiber communication.

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.

Experimental free-space continuous-variable quantum key distribution with thermal source.

Passive-state-preparation (PSP) continuous-variable quantum key distribution (CVQKD) protocol explores the intrinsic field fluctuations of a thermal source. Compared with traditional Gaussian-modulated coherent-state CVQKD, it does not need active modulations and has promising applications in chip integration and portable free-space quantum key distribution. In this Letter, we propose and experimentally realize a PSP CVQKD scheme with transmitted local oscillator (LO) through fluctuating transmittance free-space channel using an off-the-shelf amplified spontaneous emission source for the first time. By proposing thermal-state polarization multiplexing transmitted LO, synchronized channel transmittance monitoring and fine-grained phase compensation techniques, secure keys within -15 dB transmittance of simulated free-space channel with turbulence are generated, with a final average secure key rate of 1.015 Mbps asymptotically. Equivalent atmospheric turbulence model analysis shows that the free-space PSP CVQKD scheme provides a promising outlook for high-speed and chip-based CVQKD for kilometer-level atmospheric channel networks.

Analysis of the Effects of the Two-Photon Temporal Distinguishability on Measurement-Device-Independent Quantum Key Distribution

Measurement-device-independent quantum key distribution (MDI-QKD) protects legitimate users from attacks on measurement devices. The decoy method allows for unconditionally secure quantum key generation using lasers. One of the most important issues in MDI-QKD is that photons from two independent lasers must be indistinguishable. Because Alice and Bob send Charlie laser pulses through separate fiber links, the arrival times of the pulses fluctuate independently. According to the Hong-Ou-Mandel (HOM) interference at Charlie's relay, the time delay between two photons has the greatest effect on distinguishability. However, to date, these effects have not been analyzed. Our study uses simulations to investigate the effects of two-photon temporal distinguishability in terms of the visibility of the HOM-dip of two photons on the final key rate of finite-size MDI-QKD. Furthermore, an acceptable time delay range was estimated based on photons with Gaussian spectral amplitude functions.

Real-time post-processing for physical-layer secure key distribution in fiber networks

Physical-layer secure key distribution (PLSKD) in fiber networks provides robust security and full compatibility with current fiber infrastructure. The post-processing is generally required to improve the key consistency, security, and randomness in PLSKD. However, offline digital signal processing was generally adopted in the previous PLSKD schemes, while the real-time high-speed post-processing is necessary towards the practical PLSKD applications. In this paper, a real-time pipeline post-processing is designed and demonstrated using field-programmable gate array (FPGA) boards. A complete set of post-processing is applied, including double-threshold quantization, information reconciliation (IR) with Bose–Chaudhuri–Hocquenghem code, and privacy amplification (PA) with SM3 hash algorithm. The system architecture is detailed by combining all these processing steps, where the trade-offs for the post-processing scheme are analyzed. We also assess the performance of post-processing implementation on FPGA in terms of throughput and hardware resource utilization. The throughput of post-processing is optimized by pipeline design approach with the parallel processing capability of FPGA, where the maximum data throughputs are 50, 57.1, and 332.5 Mb/s for the quantization, IR, and PA, respectively. On the FPGA platform, the final key rate is up to 12.2 Mb/s. The proposed real-time post-processing FPGA prototype is a good candidate for the practical application of PLSKD in fiber networks.

Optimised Multithreaded CV-QKD Reconciliation for Global Quantum Networks

Designing a practical Continuous Variable (CV) Quantum Key Distribution (QKD) system requires an estimation of the quantum channel characteristics and the extraction of secure keys based on a large number of distributed quantum signals. On standard processors, it can take hours to reconcile the required number of quantum signals. This problem is exacerbated for Low Earth Orbit (LEO) satellite CV-QKD, where the satellite flyover time is less than a few minutes. A potential solution is massive parallelisation of the classical reconciliation where a large-code block is subdivided into many shorter blocks for individual decoding. However, the penalty of this procedure on the important final secured key rate is non-trivial to determine and hitherto has not been formally analysed. In this work, we fill this important knowledge gap via detailed analyses and experimental verification of a CV-QKD sliced reconciliation protocol that uses large block-length low-density parity-check decoders. Our new solution results in a significant increase in the final key rate relative to non-optimised reconciliation. In addition, it allows for the acquisition of quantum secured messages between terrestrial stations and LEO satellites within a flyover timescale even using off-the-shelf processors. Our work allows for optimised global quantum networks secured via fundamental physics.

Continuous-variable quantum key distribution with low-complexity information reconciliation.

Information reconciliation is an essential step of continuous-variable quantum key distribution (CV-QKD) because its efficiency affects both the maximum transmission distance and the final secret key rate of the whole system. Slice reconciliation can achieve high secret key rates for the CV-QKD systems under high signal-to-noise ratios (SNRs). However, it suffers from the high designing cost of the error-correcting codes in the multi-level coding and multi-stage decoding step. To reconcile one set of data with fixed SNR, multiple error-correcting codes with different code rates need to be designed. If the channel environment changed, the code rates need to change along to maintain high reconciliation efficiency, making it complicated and costly. In this paper, we introduce polar codes into slice reconciliation and proposed a scheme that is simply constructed, effectively performed, and well adapted to the systems with wide-range and variational SNRs. Simulation results show that the proposed scheme offers reconciliation efficiency over 95% for the systems with SNRs range from 1 to 10, which can support the systems with high secret key rates. The decrease of complexity and the increase of secret key rate have great significance for a practical CV-QKD system.

Measurement-Device-Independent Quantum Key Agreement against Collective Noisy Channel

Quantum key agreement (QKA) permits participants to constitute a shared key on a quantum channel, while no participants can independently determine the shared key. However, existing Measurement-device-independent (MDI) protocols cannot resist channel noise, and noise-resistant QKA protocols cannot resist side-channel attacks caused by equipment defects. In this paper, we design a MDI-QKA protocol against collective-dephasing noise based on GHZ states. First, in our protocol, Alice and Bob prepare a certain number of GHZ states respectively, and then send two particles of each GHZ state to Charlie for bell measurement. Results are that Alice and Bob can obtain Bell states through entanglement exchange with the help of dishonest Charlie. Meanwhile our protocol can ensure the transmission process noise-resisted. Then, Alice and Bob encode their key components to the particle in their hands and construct logical quantum states against collective noise through additional particles and CNOT operation to implement MDI-QKA. Compared with existing MDI-QKA protocols, our protocol uses logical quantum states during particle transmission, which makes the protocol immune to collective-dephasing noise and thus improves the final key rate. Security analysis shows that our protocol can resist common insider and outsider attacks.

Measurement-device-independent quantum key distribution protocol with phase post-selection

Measurement-device-independent quantum key distribution (MDI-QKD) protocol can remove all the loopholes of the detection devices and, thus, has attracted much attention. Based on the technique of single-photon interference, we propose a modified MDI-QKD protocol with phase post-selection. We prove the security of the announcement of the private phases in the X basis and show how to apply the phase post-selection method to the double-scanning four-intensity MDI-QKD protocol. The numerical results show that the phase post-selection method can significantly improve the key rates at all distances. In the double-scanning method, two parameters need to be scanned in the calculation of the final key rate, and the global parameter optimization is pretty time-consuming. We propose an accelerated method that can greatly reduce the running time of the global parameter optimization program. This makes the method practically useful in an unstable channel.

Improved polar-code-based efficient post-processing algorithm for quantum key distribution

Combined with one-time pad encryption scheme, quantum key distribution guarantees the unconditional security of communication in theory. However, error correction and privacy amplification in the post-processing phase of quantum key distribution result in high time delay, which limits the final secret key generation rate and the practicability of quantum key distribution systems. To alleviate this limitation, this paper proposes an efficient post-processing algorithm based on polar codes for quantum key distribution. In this algorithm, by analyzing the channel capacity of the main channel and the wiretap channel respectively under the Wyner’s wiretap channel model, we design a codeword structure of polar codes, so that the error correction and privacy amplification could be completed synchronously in a single step. Through combining error correction and privacy amplification into one single step, this efficient post-processing algorithm reduces complexity of the system and lower the post-processing delay. Besides, the reliable and secure communicaiton conditions for this algorithm has been given in this paper. Simulation results show that this post-processing algorithm satisfies the reliable and secure communication conditions well.

Weak Randomness Analysis of Measurement-Device-Independent Quantum Key Distribution with Finite Resources

The ideal quantum key distribution (QKD) protocol requires perfect random numbers for bit encoding and basis selecting. Perfect randomness is of great significance to the practical QKD system. However, due to the imperfection of practical quantum devices, an eavesdropper (Eve) may acquire some random numbers, thus affecting the security of practical systems. In this paper, we analyze the effects of the weak randomness in the measurement-device-independent QKD (MDI-QKD) with finite resources. We analytically derive concise formulas for estimating the lower bound of the single-photon yield and the upper bound of the phase error rate in the case of the weak randomness. The simulation demonstrates that the final secret key rate of MDI-QKD with finite resources is sensitive to state preparation, even with a small proportion of weak randomness, the secure key rate has a noticeable fluctuation. Therefore, the weak randomness of the state preparation may bring additional security risks. In order to ensure the practical security of the QKD system, we are supposed to strengthen the protection of state preparation devices.

Practical underwater quantum key distribution based on decoy-state BB84 protocol.

Polarization encoding quantum key distribution has been proven to be a reliable method to build a secure communication system. It has already been used in an inter-city fiber channel and near-Earth atmosphere channel, leaving an underwater channel the last barrier to conquer. Here we demonstrate a decoy-state BB84 quantum key distribution system over a water channel with a compact system design for future experiments in the ocean. In the system, a multiple-intensity modulated laser module is designed to produce the light pulses of quantum states, including signal state, decoy state, and vacuum state. Classical communication and synchronization are realized by wireless optical transmission. Multiple filtering techniques and wavelength division multiplexing are further used to avoid cross talk of different lights. We test the performance of the system and obtain a final key rate of 245.6 bps with an average quantum bit error rate of 1.91% over a 2.4 m water channel, in which the channel attenuation is 16.35 dB. Numerical simulation shows that the system can tolerate up to 21.7 dB total channel loss and can still generate secure keys in 277.9 m Jerlov type I ocean channel.

A robust quantum private query based on six-qubit with decoherence

In order to deal with the error of oblivious key distribution caused by quantum channel noise, a new quantum privacy query (QPQ) protocol with six-qubit with decoherence is proposed. When the error rate caused by quantum channel noise is less than 30%, the final key bit error rate of this protocol is better than that of other QPQ protocols using the same post-processing algorithm. Furthermore, the protocol is also a cheat-sensitive protocol, in which dishonesty of either party can be detected.

QKD key generation control protocol

Polarization-encoding fiber QKD requires compensation of polarization distortion caused by birefringence in optical fiber. Solving this task inevitably requires losing some effectiveness in terms of the final key rate. In this work, a time-division multiplexing protocol for polarisation calibration is suggested. This protocol was implemented in a QRate commercial QKD fiber system, utilizing BB84-protocol. Parameters of the protocol were optimized to maximize the secret key rate.

Airborne quantum key distribution with boundary layer effects

With the substantial progress of terrestrial fiber-based quantum networks and satellite-based quantum nodes, airborne quantum key distribution (QKD) is now becoming a flexible bond between terrestrial fiber and satellite, which is an efficient solution to establish a mobile, on-demand, and real-time coverage quantum network. However, the random distributed boundary layer is always surrounded to the surface of the aircraft when the flight speed larger than 0.3 Ma, which would introduce random wavefront aberration, jitter and extra intensity attenuation to the transmitted photons. In this article, we propose a performance evaluation scheme of airborne QKD with boundary layer effects. The analyzed results about the photon deflection angle and wavefront aberration effects, show that the aero-optical effects caused by the boundary layer can not be ignored, which would heavily decrease the final secure key rate. In our proposed airborne QKD scenario, the boundary layer would introduce ∼3.5 dB loss to the transmitted photons and decrease ∼70.9% of the secure key rate. With tolerated quantum bit error rate set to 8%, the suggested quantum communication azimuth angle between the aircraft and the ground station is within 55∘. Furthermore, the optimal beacon laser module and adaptive optics module are suggested to be employed, to improve the performance of airborne QKD system. Our detailed airborne QKD performance evaluation study can be performed to the future airborne quantum communication designs.

Practical Long‐Distance Measurement‐Device‐Independent Quantum Key Distribution By Four‐Intensity Protocol

AbstractQuantum key distribution (QKD) can provide unconditionally secure private communication between two remote parties. The measurement‐device‐independent (MDI) QKD can remove all security loopholes in measurement devices. However, the large value of the observed error rate in X basis has severely limited its key rate. The four‐intensity protocol with fully optimized post data processing can improve the key rate and distance of MDI‐QKD effectively. In this paper, the four‐intensity MDI‐QKD protocol is reviewed. In the four‐intensity protocol, each of Alice and Bob uses one intensity in Z basis and three intensities in X basis (normally including one vacuum). This improves the number of effective bits in Z basis. The joint mathematical treatment for statistical fluctuation and the parameter scan pointing directly to the final key rate are applied to reduce the effect of statistical fluctuation. The double scanning method further improves the key rate and the secure distance of the four‐intensity protocol. These have greatly improved the performance of the protocol with finite‐key effects. So far, many MDI‐QKD experiments are based on the four‐intensity protocol. The successful results of these experiments have clearly shown the superiority of the four‐intensity protocol in practical long‐distance MDI‐QKD.

Secure quantum secret sharing without signal disturbance monitoring.

Quantum secret sharing (QSS) is an essential primitive for the future quantum internet, which promises secure multiparty communication. However, developing a large-scale QSS network is a huge challenge due to the channel loss and the requirement of multiphoton interference or high-fidelity multipartite entanglement distribution. Here, we propose a three-user QSS protocol without monitoring signal disturbance, which is capable of ensuring the unconditional security. The final key rate of our protocol can be demonstrated to break the Pirandola-Laurenza-Ottaviani-Banchi bound of quantum channel and its simulated transmission distance can approach over 600 km using current techniques. Our results pave the way to realizing high-rate and large-scale QSS networks.

Strengthening practical continuous-variable quantum key distribution against measurement angular error.

The optical phase shifter that constantly rotates the local oscillator phase is a necessity in continuous-variable quantum key distribution systems with heterodyne detection. In previous experimental implementations, the optical phase shifter is generally regarded as an ideal passive optical device that perfectly rotates the phase of the electromagnetic wave of 90∘. However, the optical phase shifter in practice introduces imperfections, mainly the measurement angular error, which inevitably deteriorates the security of the practical systems. Here, we will give a concrete interpretation of measurement angular error in practical systems and the corresponding entanglement-based description. Subsequently, from the parameter estimation, we deduce the overestimated excess noise and the underestimated transmittance, which lead to a reduction in the final secret key rate. Simultaneously, we propose an estimation method of the measurement angular error. Next, the practical security analysis is provided in detail, and the effect of the measurement angular error and its corresponding compensation scheme are demonstrated. We conclude that measurement angular error severely degrades the security, but the proposed calibration and compensation method can significantly help improve the performance of the practical CV-QKD systems.