Theoretical analysis for estimating laser integrated linewidth via frequency-noise power spectral density.

The measurement of a laser linewidth is significant in metrology, coherent optical communications, high-resolution sensing, and LIDAR. Firstly, in this study, we theoretically explain why estimating an integrated linewidth via a frequency-noise power spectral density (PSD) is valid. We find that the previous methods estimating the integrated linewidth via the frequency-noise PSD result from Gaussian approximation and obtain a more general consequence. Secondly, according to the theory, we propose the Voigt approximation method to improve the estimation performance. The simulation results show the Voigt approximation estimation error is lower than 5%. Finally, based on the Voigt approximation, the relationship between the interference visibility and laser linewidth is found, providing a possible convenient approach to measuring the linewidth.

Stable and wavelength-tunable multiwavelength laser for high-rate measurement device independent quantum key distribution.

Measurement device independent quantum key distribution (MDI QKD) has attracted growing attention for its immunity to attacks at the measurement unit, but its unique structure limits the secret key rate. Utilizing the wavelength division multiplexing (WDM) technique and reducing error rates are effective strategies for enhancing the secret key rate. Reducing error rates often requires active feedback control of wavelengths using precise external references. However, for a multiwavelength laser, employing multiple references to stabilize each wavelength output places stringent demands on these references and significantly increases system complexity. Here, we demonstrate a stable, wavelength-tunable multiwavelength laser with an output wavelength ranging from 1270 to 1610 nm. Through precise temperature control and stable drive current, we passively lock the laser wavelength, achieving remarkable wavelength stability. This significantly reduce the error rate, leading to an almost doubling of the secret key rate compared to previous experiments. Furthermore, the exceptional wavelength stability offered by our multiwavelength laser, combined with the WDM technique, has further boosted the secret key rate of MDI QKD. With a wide wavelength tuning range of 5.1 nm, our multiwavelength laser facilitates flexible operation across multiple dense wavelength division multiplexing channels. Coupled with high wavelength stability and multiple wavelength outputs simultaneously, this laser offers a promising solution for a high-rate MDI QKD system.

Practical semi-quantum key distribution with one-way key and one basis.

Semi-quantum key distribution (SQKD) protocols are used to distribute secret keys between a quantum party and a classical party. However, existing SQKD protocols rely on two-way communication, and may still be vulnerable to Trojan horse side-channel attacks where Eve sends her own photon into a receiver's apparatus and measures the reflected photon to estimate the key. In this paper, we propose a practical SQKD with one-way key. This requires that the single photons travelling through the one-way channel are used to encode bit information, and the returned photons are used to quantify Eve's information, thus reducing the security analysis of the Trojan horse attack in SQKD. Meanwhile, our protocol with one basis enjoys security advantage in practical SQKD systems when source flaws are taken into account. In particular, the present protocol is secure under practical conditions when weak coherent pulses (WCP) are used. Our simulation results show that the protocol using WCP can distribute secret keys over a distance of 110 km without decoy states.

Experimental Demonstration of Fully Passive Quantum Key Distribution.

The passive approach to quantum key distribution (QKD) consists of removing all active modulation from the users' devices, a highly desirable countermeasure to get rid of modulator side channels. Nevertheless, active modulation has not been completely removed in QKD systems so far, due to both theoretical and practical limitations. In this Letter, we present a fully passive time-bin encoding QKD system and report on the successful implementation of a modulator-free QKD link. According to the latest theoretical analysis, our prototype is capable of delivering competitive secret key rates in the finite key regime.

Afterpulse effects in quantum key distribution without monitoring signal disturbance.

The round-robin differential phase shift (RRDPS) quantum key distribution (QKD) protocol is the only one that does not require monitoring of signal disturbance. Moreover, it has been proven that RRDPS has excellent performance of resistance to finite-key effects and high error rate tolerance. However, the existing theories and experiments do not take the afterpulse effects into account, which cannot be neglected in high-speed QKD systems. Here, we propose a tight finite-key analysis with afterpulse effects. The results show that the non-Markovian afterpulse RRDPS model optimizes the system performance considering afterpulse effects. The advantage of RRDPS over decoy-state BB84 under short-time communication still holds at typical values of afterpulse.

General temporal ghost imaging model with detection resolution and noise.

Improving imaging quality while reducing the sampling time simultaneously is a crucial challenge that limits the practical application of temporal ghost imaging (TGI). To improve the performance of TGI, various methods have been proposed and verified. However, a work analyzing in detail the influence of intensity accuracy and detection noise of TGI is still absent. Here, we establish an evaluation model to quantify the imaging quality of TGI and differential TGI (DTGI). Our model considers the intensity detection accuracy, threshold, and noise of the test path during image reconstruction and quantifies their influences by developing general imaging formulas of (D)TGI. We also simulate the imaging of (D)TGI numerically. The evaluation demonstrates that (D)TGI is relatively not sensitive to detection accuracy and thresholds of the test path, and image quality is degraded slightly even when those parameters turn much worse. (D)TGI is relatively robust to detection noise but will be unable to reconstruct the object when noise is too strong. DTGI does not show clear advantages over TGI. Our work develops an effective model to quantify the image quality with practical parameters and is significant to real applications of (D)TGI.

Finite-Key Analysis for Quantum Key Distribution with Discrete-Phase Randomization.

Quantum key distribution (QKD) allows two remote parties to share information-theoretic secret keys. Many QKD protocols assume the phase of encoding state can be continuous randomized from 0 to 2π, which, however, may be questionable in the experiment. This is particularly the case in the recently proposed twin-field (TF) QKD, which has received a lot of attention since it can increase the key rate significantly and even beat some theoretical rate-loss limits. As an intuitive solution, one may introduce discrete-phase randomization instead of continuous randomization. However, a security proof for a QKD protocol with discrete-phase randomization in the finite-key region is still missing. Here, we develop a technique based on conjugate measurement and quantum state distinguishment to analyze the security in this case. Our results show that TF-QKD with a reasonable number of discrete random phases, e.g., 8 phases from {0,π/4,π/2,…,7π/4}, can achieve satisfactory performance. On the other hand, we find the finite-size effects become more notable than before, which implies that more pulses should be emit in this case. More importantly, as a the first proof for TF-QKD with discrete-phase randomization in the finite-key region, our method is also applicable in other QKD protocols.

Imperfection-insensitivity quantum random number generator with untrusted daily illumination.

Quantum random number generators (QRNGs) promise secure randomness generation based on the foundational unpredictability of quantum mechanics. However, the unavoidable gaps between theoretical models and practical devices could lead to security invalidation. Recently, a source-independent quantum random number generator (SI-QRNG) has been proposed to solve the issue of uncharacteristic sources. However, in most current analyses of SI-QRNG protocols, the security proofs with imperfect measurements are individual for different factors and very sensitive to small deviations from theoretical models. Here, we establish a unified model for imperfect measurements in the SI-QRNG and provide a tight rate bound based on the uncertainty relation for smooth entropies. Then the performance with large device imperfections is evaluated and the randomness rate in our model can approach a similar order of magnitude of the rate upper bound in common discrete variable QRNGs. In addition, by utilizing the daily illumination and measurement devices with large imperfections, we experimentally demonstrate our scheme at the rate of the order of magnitude of Mbps.

Transmittance-invariant phase modulator for chip-based quantum key distribution.

In chip-based quantum key distribution (QKD) systems, the non-ideal quantum state preparation due to the imperfect electro-optic phase modulators (EOPM) decreases the secret key rate and introduces potential vulnerabilities. We propose and implement an on-chip transmittance-invariant phase modulator (TIPM) to solve this problem. Simulated and experimental results show that TIPM can eliminate the correlation between phase, intensity, and polarization of quantum states caused by phase-dependent loss. The design can tolerate a significant fabrication mismatch and is universal to multi-material platforms. Furthermore, TIPM increases the modulation depth achievable by EOPMs in standard process design kit (PDK). The proposal of TIPM can improve the practical security and performance of the chip-based QKD systems.

Afterpulse effect in measurement-device-independent quantum key distribution.

There is no doubt that measurement-device-independent quantum key distribution (MDI-QKD) is a crucial protocol that is immune to all possible detector side channel attacks. In the preparation phase, a simulation model is usually employed to get a set of optimized parameters, which is utilized for getting a higher secure key rate in reality. With the implementation of high-speed QKD, the afterpulse effect which is an intrinsic characteristic of the single-photon avalanche photodiode is no longer ignorable, this will lead to a great deviation compared with the existing analytical model. Here we develop an afterpulse-compatible MDI-QKD model to get the optimized parameters. Our results indicate that by using our afterpulse-compatible model, we can get a much higher key rate than the prior afterpulse-omitted model. It is significant to take the afterpulse effect into consideration because of the improvement of the system working frequency.

Certified Randomness from Untrusted Sources and Uncharacterized Measurements.

Generating random numbers plays an important role in many scientific applications. Compared to pseudorandom number generators, a quantum device is capable of generating true random numbers by the laws of quantum mechanics. However, information-theoretical secure random numbers are regularly based on a perfect device model, which may deviate from a real-world device. To close this gap, we propose a quantum random number generation protocol and experimentally demonstrate it. In our protocol, we make no assumptions about the source. Some reasonable assumptions on the trusted two-dimensional measurement are needed, but we do not require a detailed characterization. Even if considering the most general quantum attack and using the general sources, we achieve a randomness generation rate of over 1 Mbps with a universal composable security parameter of 10^{-10}.

Integration in the C-band between quantum key distribution and the classical channel of 25 dBm launch power over multicore fiber media.

The quantum-classical coexistence can be implemented based on wavelength division multiplexing (WDM), but due to Raman noise, the wavelength spacing between quantum and classical signals and launch power from classical channels are restricted. Space division multiplexing (SDM) can now be availably achieved by multicore fiber (MCF) to reduce Raman noise, thereby loosening the restriction for coexistence in the same band and obtaining a high communication capacity. In this paper, we realize the quantum-classical coexistence over a 7-core MCF. Based on the SDM, the highest launch power of 25 dBm is achieved which has been extended nearly 19 times in previous work. Moreover, both the quantum and classical channels are allocated in the C-band and the minimum wavelength spacing between them is only 1.6 nm. The coexistence system eliminates the need for adding a narrowband filter.

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.

Compact quantum random number generation using a linear optocoupler.

To date, various quantum random number schemes have been demonstrated. However, the cost, size, and final random bit generation rate usually limits their wide application on-shelf. To overcome these limitations, we propose and demonstrate a compact, simple, and low-cost quantum random number generation based on a linear optocoupler. Its integrated structure consists mainly of a light emitting diode and a photodetector. Random bits are generated by directly measuring the intensity noise of the output light, which originates from the random recombination between holes of the p region and electrons of the n region in a light emitting diode. Moreover, our system is robust against fluctuation of the operating environment, and can be extended to a parallel structure, which will be of great significance for the practical and commercial application of quantum random number generation. After post-processing by the SHA-256 algorithm, a random number generation rate of 43 Mbps is obtained. Finally, the final random bit sequences have low autocorrelation coefficients with a standard deviation of 3.16×10-4 and pass the NIST-Statistical Test Suite test.

Coexistence of quantum key distribution and optical transport network based on standard single-mode fiber at high launch power.

There is an increasing demand for multiplexing of quantum key distribution with optical communications in single fiber in consideration of high costs and practical applications in the metropolitan optical network. Here, we realize the integration of quantum key distribution and an optical transport network of 80 Gbps classical data at 15 dBm launch power over 50 km of the widely used standard (G.652 Recommendation of the International Telecom Union Telecom Standardization Sector) telecom fiber. A secure key rate of 11 Kbps over 20 km is obtained. By tolerating a high classical optical power up to 18 dBm of 160 Gbps classical data on single-mode fiber, our result shows the potential and tolerance of quantum key distribution being used in future large capacity transmission systems, such as metropolitan area networks and data centers. The quantum key distribution system is stable, practical, and insensitive to the polarization disturbance of channels by using a phase coding system based on a Faraday-Michelson interferometer. We also discuss the fundamental limit for quantum key distribution performance in the multiplexing environment.

Quantum random number generation based on spontaneous Raman scattering in standard single-mode fiber.

We investigate quantum random number generation based on backward spontaneous Raman scattering in standard single-mode fiber, where the randomness of photon wavelength superposition and arrival time is simultaneously utilized. The experiment uses four avalanche photodiodes working in gated Geiger mode to detect backward Raman scattering photons from four different wavelength channels and a time-to-digital converter placed behind the detectors to record their arrival time. Both information of the wavelength and arrival time interval of photons from different channels are applied to generate random bits. Due to the independence of these two entropy sources, the random number resource of the present system is fully utilized. Five-bit raw data can be obtained for every effective click, which contains 2.87-bit min-entropy. To obtain the optimal generation rate of random bits, appropriate pump power and fiber length are adopted. The post-processing method by the SHA-256 hashing algorithm is used to remove the bias of the raw data, after which the final random bit sequences pass the NIST statistical test.

Finite-key analysis for twin-field quantum key distribution based on generalized operator dominance condition.

Quantum key distribution (QKD) can help two distant peers to share secret key bits, whose security is guaranteed by the law of physics. In practice, the secret key rate of a QKD protocol is always lowered with the increasing of channel distance, which severely limits the applications of QKD. Recently, twin-field (TF) QKD has been proposed and intensively studied, since it can beat the rate-distance limit and greatly increase the achievable distance of QKD. Remarkalebly, K. Maeda et. al. proposed a simple finite-key analysis for TF-QKD based on operator dominance condition. Although they showed that their method is sufficient to beat the rate-distance limit, their operator dominance condition is not general, i.e. it can be only applied in three decoy states scenarios, which implies that its key rate cannot be increased by introducing more decoy states, and also cannot reach the asymptotic bound even in case of preparing infinite decoy states and optical pulses. Here, to bridge this gap, we propose an improved finite-key analysis of TF-QKD through devising new operator dominance condition. We show that by adding the number of decoy states, the secret key rate can be furtherly improved and approach the asymptotic bound. Our theory can be directly used in TF-QKD experiment to obtain higher secret key rate. Our results can be directly used in experiments to obtain higher key rates.

Finite-key analysis for round-robin-differential-phase-shift quantum key distribution: erratum.

Two errata are presented to correct two typographical errors in our paper.

Finite-key analysis for round-robin-differential-phase-shift quantum key distribution.

Since the round-robin-differential-phase-shift (RRDPS) quantum key distribution (QKD) protocol was proposed, it has attracted much attention due to its unique characteristic i.e., it can bind the amount of information leakage without monitoring signal disturbance. Recently, Yin et al. have developed a novel theory to estimate its information leakage tightly. However, the finite-sized key effects are not taken into account. Here, we fill this gap and extend the security proof of the RRDPS protocol to the finite-sized regime using post-selection technique. As a consequence, it's predicted that the key rate of RRDPS in a finite-sized key scenario can be comparable to the asymptotic one, which is meaningful for the real-life applications.

Experimental realization of a reference-frame-independent decoy BB84 quantum key distribution based on Sagnac interferometer.

Quantum key distribution (QKD) can generate secure key bits between remote users employing the features of quantum physics. However, a shared reference frame is necessary for QKD systems in most scenarios. A reference-frame-independent (RFI) scheme can tolerate the reference frame drifting between legitimate remote users, which is significant in the operation of relative moving terminals such as satellites and aircraft. We design and experimentally demonstrate an RFI-BB84-QKD system by joint encoding with the polarization and orbital angular momentum states of the photons. We use self-compensating fiber Sagnac interferometers to perform high-speed polarization modulation, and q-plates to passively manipulate the rotation-invariant photon states, which makes the system feasible for high-speed operation using off-the-shelf components.