Reference-frame-independent Quantum Key Distribution Research Articles

Reference-frame-independent quantum key distribution with two-way classical communication

Abstract The data post-processing scheme based on two-way classical communication (TWCC) can improve the tolerable bit error rate and extend the maximal transmission distance when used in a quantum key distribution (QKD) system. In this study, we apply the TWCC method to improve the performance of reference-frame-independent quantum key distribution (RFI-QKD), and analyze the influence of the TWCC method on the performance of decoy-state RFI-QKD in both asymptotic and non-asymptotic cases. Our numerical simulation results show that the TWCC method is able to extend the maximal transmission distance from 175 km to 198 km and improve the tolerable bit error rate from 10.48% to 16.75%. At the same time, the performance of RFI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are considered. We conclude that RFI-QKD with the TWCC method is of practical interest.

Improving the performance of reference-frame-independent quantum key distribution with advantage distillation technology.

The reference-frame-independent quantum key distribution (RFI-QKD) has the advantage of tolerating reference frames that slowly vary. It can generate secure keys between two remote users with slowly drifted and unknown reference frames. However, the drift of reference frames may inevitably compromise the performance of QKD systems. In the paper, we employ the advantage distillation technology (ADT) to the RFI-QKD and the RFI measurement-device-independent QKD (RFI MDI-QKD), and we then analyze the effect of ADT on the performance of decoy-state RFI-QKD and RFI MDI-QKD in both asymptotic and nonasymptotic cases. The simulation results show that ADT can significantly improve the maximum transmission distance and the maximum tolerable background error rate. Furthermore, the performance of RFI-QKD and RFI MDI-QKD in terms of the secret key rate and maximum transmission distance are still greatly improved when statistical fluctuations are taken into account. Our work combines the merits of the ADT and RFI-QKD protocols, which further enhances the robustness and practicability of QKD systems.

Reference-frame-independent quantum key distribution with advantage distillation.

Advantage distillation (AD) provides a means of separating highly correlated raw key bits from weakly correlated information in quantum key distribution (QKD). In this Letter, we apply the AD method to improve the performance of reference-frame-independent QKD (RFI-QKD). Simulation results show that, compared with RFI-QKD without AD, RFI-QKD with AD can tolerate higher system errors and obtain better performance on the secret key rate and transmission distance. Furthermore, we extend the AD method to RFI measurement-device-independent QKD (RFI-MDI-QKD) and demonstrate that the AD method can improve the performance of RFI-MDI-QKD more significantly.

Reference-frame-independent quantum key distribution based on passive light source monitoring

In quantum key distribution (QKD), the users need to share the same reference frame. If their reference frames are inconsistent, the QKD system will not function properly. The most widely used method today is the active real-time calibration of both communication reference frames by using classical communication. In order to get rid of the real-time calibration operation of the reference frames, a QKD protocol independent of reference frame is proposed, called reference-frame-independent QKD (RFI-QKD). The RFI-QKD protocol is immune to the effects of slowly changing reference frame drift, requiring that only one set of bases should be aligned by Alice and Bob, and the remaining two sets of bases can slowly change in the channel. In the real QKD system, a set of basis vectors can always be found to maintain a stable alignment. However, some assumptions are made for the sources in most reported researches, i.e. with a trusted and fixed photon-number distribution (PND), which usually cannot be satisfied in practical implementations. Those unreasonable assumptions will inevitably compromise the security of practical QKD systems. To solve the problem, in this work, we present a passive light source monitoring (PLSM) scheme for RFI-QKD, which is accomplished by a passive monitoring module consisting of a beam splitter and two detectors on the source side. Through the PLSM module, we can have four monitoring events by using two local detectors and then precisely estimate the bounds of source distributions. Specifically, we take the three-intensity decoy-state-based RFI-QKD for example for illustraing the events. Compared with the original RFI-QKD, our PLSM method can passively monitor the PND and has many advantages, with light source fluctuations, finite-size effects and reference frame deflection angles taken into account.

Experimental demonstration of tomography-based quantum key distribution.

Tomography is a very beneficial and fundamental technique in the fields of quantum information and quantum optics, which can be applied to infer information about quantum states or quantum processes. In quantum key distribution (QKD), tomography can be proposed to improve the secure key rate by taking full advantage of data from both matched and mismatched measurement outcomes to characterize quantum channels accurately. However, to date, no experimental work has been conducted on it. In this work, we study tomography-based QKD (TB-QKD), and for the first time, to the best of our knowledge, carry out proof-of-principle experimental demonstrations by implementing Sagnac interferometers to simulate different transmission channels. Furthermore, we compare it with reference-frame-independent QKD (RFI-QKD) and demonstrate that TB-QKD can significantly outperform RFI-QKD in certain channels, e.g., amplitude damping channel or probabilistic rotation channel.

Free-running long-distance reference-frame-independent quantum key distribution

AbstractRapidly and randomly drifted reference frames will shorten the transmission distance and decrease the secure key rate of realistic quantum key distribution (QKD) systems. In this article, we present a free-running reference-frame-independent (RFI) QKD scheme, where measurement events are classified into multiple slices with similar estimated classification parameter. We perform the free-running RFI QKD experiment with a fiber link of 100 km and reference frame misalignment more than 29 periods in 50.7 h. A key rate as high as 742.98 bps is achieved at the total loss of 31.5 dB benefiting from both the new protocol design and the 80 MHz repetition rate system in use. Our system runs 50.7 h freely without any reference frame alignment. In the experiment, the misalignment variation rate tolerance of the experiment is 0.262 rad/s, and could be optimized to 1.309 rad/s. Therefore, our free-running RFI scheme can be efficiently adapted into the satellite-to-ground and drone-based mobile communication scenarios.

Improved reference-frame-independent quantum key distribution

Reference-frame-independent quantum key distribution (RFI-QKD) can generate secure keys between two remote peers with an unknown and slowly drifted reference frame. It adopts a statistical quantity C independent of the rotation of the reference frame to estimate the eavesdropper’s knowledge. However, in practical scenarios, the estimation of C should be completed with data collected in a short period of time, since the variation of the reference frame during the run will smear its correlations. In this paper, we propose to improve the performance of RFI-QKD with a new, to the best of our knowledge, statistical quantity R, which is less sensitive to statistical fluctuations and more robust to the variation of the reference frame, and obtain an analytical bound to estimate the eavesdropper’s knowledge. Simulation results show that the performance of RFI-QKD in the non-asymptotic case can be significantly promoted, which is very promising in practical QKD systems. Furthermore, we apply the new statistical quantity R to the RFI measurement-device-independent QKD (RFI-MDI-QKD) protocol and demonstrate that significant improvement can also be obtained in RFI-MDI-QKD.

Security of reference-frame-independent quantum key distribution with source flaws

Recently, reference-frame-independent quantum key distribution (RFI-QKD) has attracted more attention, since no active calibration of the reference frame is required. Thus, it has potential advantages in practical applications, especially for QKD with a mobile-platform-based quantum channel. However, due to the imperfections of devices, practical security is still one of the main bottlenecks for the application of RFI-QKD. Although, based on ``qubit'' assumption, RFI-QKD with the inaccuracy of encoded state was analyzed and demonstrated, this assumption is hard to be guaranteed in practical situations, and some source flaws could not be considered. In this paper we evaluate the security of RFI-QKD with general source flaws, in which the qubit assumption is removed. Then, almost all the source flaws (not only the inaccuracy of encoded state, but also the side channel, the Trojan horse, and so on) can be considered together.

Countermeasure for security loophole caused by asymmetric correlations of reference frame independent quantum key distribution with fewer quantum states.

One of the challenging issues in free-space quantum key distribution (QKD) is the requirement of active compensation of the reference frame between the transmitter and receiver. Reference frame independent (RFI) QKD removes active compensation, but it requires more quantum states. A recent proposal can effectively reduce the required quantum states, but this can be achieved assuming the correlations defined in RFI QKD are symmetric. In a real QKD system, such symmetric correlations cannot always be satisfied owing to the device imperfections and optical misalignment. We theoretically analyze the effect of asymmetric correlations. Consequently, we report that the asymmetry causes security loopholes and provide a countermeasure to prevent them. Furthermore, we provide the experimental results of a free-space RFI QKD system to verify the countermeasure for the aforementioned problem. In conclusion, our work provides feasibility of the practical RFI QKD system with fewer quantum states by effectively preventing the security loophole.

Reference-frame-independent quantum key distribution of wavelength division multiplexing with multiple quantum channels* *Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 2019XD-A02), the State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications (BUPT) (Grant No. IPOC2021ZT10), and BUPT Innovation and Entrepreneurship Support Program (Grant No. 2021-YC-A315).

Reference-frame-independent quantum key distribution (RFI-QKD) can allow a quantum key distribution system to obtain the ideal key rate and transmission distance without reference system calibration, which has attracted much attention. Here, we propose an RFI-QKD protocol based on wavelength division multiplexing (WDM) considering finite-key analysis and crosstalk. The finite-key bound for RFI-QKD with decoy states is derived under the crosstalk of WDM. The resulting secret key rate of RFI-QKD, which is more rigorous, is obtained. Simulation results reveal that the secret key rate of RFI-QKD based on WDM is affected by the multiplexing channel number, as well as crosstalk between adjacent channels.

Performance of reference-frame-independent quantum key distribution in underwater channel

During free-space quantum key distribution, the rotation and fluctuation of reference frame degrades the performance of quantum key distribution (QKD). Reference-frame-independent QKD (RFI-QKD) overcomes this issue effectively. To date, much theoretical and experimental research has been conducted on the performance of free-space RFI-QKD. However, these studies are all based on free-space air and satellite ground, and none have investigated the performance of RFI-QKD in an underwater channel. Therefore, this paper constructed a channel model that considered both scattering and optical attenuation to obtain an RFI-QKD secret key rate in an underwater channel. The simulation results confirm that even in a relatively harsh underwater scenario, RFI-QKD maintains good performance.

Improving the performance of reference-frame-independent quantum key distribution through a turbulent atmosphere

Reference-frame-independent quantum key distribution (RFI-QKD) can dispense with the requirements of active alignment on reference frames between legitimate users, which is beneficial for free-space implementation. However, the fluctuating transmittance due to atmospheric turbulence still remains a great challenge for improving the performance and has been seldom addressed. In this paper we extend the recently proposed prefixed-threshold real-time selection method to RFI-QKD while combining practical consideration of the transmittance probability distribution model based on the finite aperture theory. Through numerical simulations, we present an estimation for the variance of the log-normal model with respect to distance and receiving aperture radius, and demonstrate the effectiveness of using this method in the RFI protocol. Considering the finite-key effects, simulation results show that the gap of the key rate with different reference frame deviations can be alleviated by increasing the data size. By adopting this method one can tolerate more serious transmission loss, especially in strong turbulence cases, which is helpful for future free-space experimental designs.

Reference-frame-independent quantum key distribution with random atmospheric transmission efficiency

Reference-frame-independent quantum key distribution (RFI-QKD) has been proved to be tolerant against unknown reference frame misalignment, which reserves interesting prospects in implementing global quantum communication. However, few works have been addressed on the performance and feasibility for RFI-QKD in turbulent atmospheric channels. Here, we propose to implement RFI-QKD in practical free-space links with fluctuating transmission efficiency due to beam wandering and broadening. An improved model for estimating the probability distribution of single-photon receiving efficiency has been developed and we also simulated the Gaussian beam spot evolution and secure key rate based on that. Results show that the beam wandering model of probability distribution of transmission efficiency is reasonable to improve the performance of RFI-QKD in free-space channel.

Reference-Frame-Independent Quantum Key Distribution in Uplink and Downlink Free-Space Channel

The reference-frame-independent quantum key distribution (RFI-QKD) allows the authorized users to share secrete keys without active alignment of the reference frames, which is beneficial for the implementation over free-space channel. However, the performance of free-space RFI-QKD could notably degrade due to the influence of atmospheric conditions. In this paper, we investigate the transmission attenuation of free-space channel in uplink and downlink scenario, respectively. Furthermore, we also simulate the relationships between the diffraction-caused attenuation and the apertures of sending and receiving optics. Then, the key generation rate of RFI-QKD and BB84 protocol are compared in different links with reference frame deviations. Simulation results show that the transmission attenuation due to diffraction can be reduced by choosing appropriate optical apertures, and better performance of free-space RFI-QKD can be achieved in downlink configuration.

Field demonstration of time-bin reference-frame-independent quantum key distribution via an intracity free-space link.

Free-space quantum key distribution (QKD) based on mobile platforms, such as satellites, drones, and vehicles, is considered a promising way to overcome the rate-distance limit without a quantum repeater. Real-time reference frame calibration is required in most recent implemented polarization encoded QKD systems due to the relative motion between sender and receiver. Although active compensations can be used to calibrate the reference frame, doing so increases the complexity of the system and reduces the key rate. To overcome this problem, the reference-frame-independent (RFI) QKD was proposed in which fixed deviations of the reference frame between the two parties are tolerated automatically. In this Letter, we report the experimental implementation of a time-bin encoded RFI QKD in an urban environment through free space. The quantum bit error rate for key-distill is as low as 1% over a 2 km free-space link with a total equivalent loss of 31.5 dB. Our demonstration shows that a stable RFI QKD can be implemented in the free-space channel.

One-decoy state reference-frame-independent quantum key distribution* *Project supported by the National Key Research and Development Program of China (Grant Nos. 2018YFA0306400 and 2017YFA0304100), the National Natural Science Foundation of China (Grant Nos. 61590932, 11774180, and 61705110), and the Natural Science Foundation of Jiangsu Province for Leadingedge Technology Program, China (Grant No. BK20192001).

Reference-frame-independent quantum key distribution (RFI-QKD) has been proven to be very useful and practical under realistic environment. Here, we present a scheme for one-decoy state RFI-QKD based on the work of Rusca et al. [Appl. Phys. Lett. 112, 171104 (2018)], and carry out investigation on its performance under realistic experimental conditions. Numerical simulation results show that the one-decoy state RFI-QKD can achieve comparable performance in terms of secret key rate and transmission distance as the two-decoy state correspondence under practical experimental conditions. On contrast, it does not need to prepare the vacuum state in the former case, substantially reducing the experimental complexity and random number consumptions. Therefore, our present proposal seems very promising in practical implementations of RFI-QKD.

Reference-frame-independent, measurement-device-independent quantum key distribution using fewer quantum states.

Reference-frame-independent quantum key distribution (RFI-QKD) provides a practical way to generate secret keys between two remote parties without sharing common reference frames. On the other hand, measurement-device-independent QKD (MDI-QKD) offers a high level of security, as it is immune to all quantum hacking attempts to measurement devices. The combination of these two QKD protocols, i.e., RFI-MDI-QKD, is one of the most fascinating QKD protocols, since it holds advantages of both practicality and security. For further practicality of RFI-MDI-QKD, it is beneficial to reduce the implementation complexity. Here, we show that RFI-MDI-QKD can be implemented using fewer quantum states than those of its original proposal. We find that, in principle, the number of quantum states for one of the parties can be reduced from six to three without compromising security. Compared to conventional RFI-MDI-QKD where both parties transmit six quantum states, it significantly simplifies the implementation of the QKD protocol. We also verify the feasibility of the scheme with a proof-of-principle experiment.

Reference-frame-independent quantum key distribution with an untrusted source**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002) and the National Natural Science Foundation of China (Grant Nos. 61505261, 61675235, 61605248, and 11304397).

Reference frame independent quantum key distribution (RFI-QKD) allows two legitimate parties to share the common secret keys with the drift of reference frames. In order to reduce the actual requirements of RFI-QKD protocol on light source and make it more suitable for practical applications, this paper gives a specific description of RFI-QKD protocol with an untrusted source and analyzes the practical security of this protocol based on the two-way “plug and play” structure commonly used in practical systems. In addition, we also investigate the performance of RFI-QKD with an untrusted source considering statistical fluctuations based on Chernoff bound. Using simulations, we compare the secret key rate of RFI-QKD with an untrusted source to RFI-QKD with trusted source. The results show that the performance of RFI-QKD with an untrusted source is similar to that of RFI-QKD with trusted source, and the finite data size clearly effects the performance of our protocol.

Decoy-state reference-frame-independent quantum key distribution with the heralded pair-coherent source

Reference-frame-independent quantum key distribution (RFI-QKD) can generate secure keys without the alignment of reference frames. Here, we propose to realize RFI-QKD with the heralded pair-coherent source (HPCS). Simulation results show that, considering the statistical fluctuations (e.g., the Gaussian distribution assumption of the channel fluctuations), the performance of RFI-QKD with HPCS outperforms that of the weak coherent source.

Experimental study of four-state reference-frame-independent quantum key distribution with source flaws

Reference-frame-independent quantum key distribution (RFI-QKD) has been proposed as a method to avoid the requirement of real-time alignment of reference frames. However, the source flaw has not been considered in most of the previously reported works. In this paper, based on the analysis of Wang et al. [Phys. Rev. A 92, 042319 (2015)], we perform a proof-of-concept experiment to demonstrate the loss-tolerant RFI-QKD by constructing a time-bin phase-encoded system and quantifying its source flaws. Moreover, the finite-key analysis is taken into account while estimating the secure key rate. Our experimental demonstration makes a positive contribution to the realization of quantum cryptography in a complex and imperfect real-world environment.