Decoy-state Research Articles

Practical Analysis of Sending or Not-Sending Twin-Field Quantum Key Distribution with Frequency Side Channels

The twin-field quantum key distribution (TF-QKD) and its variants can overcome the fundamental rate-distance limit of QKD. However, their physical implementations with the side channels remain the subject of further research. We test the side channel of a type of external intensity modulation that applies a Mach–Zehnder-type electro-optical intensity modulator, which shows the distinguishability of the signal and decoy states in the frequency domain. Based on this security loophole, we propose a side-channel attack, named the passive frequency-shift attack, on the imperfect implementation of the sending or not-sending (SNS) TF-QKD protocol. We analyze the performance of the SNS protocol with the actively odd-parity pairing (AOPP) method under the side-channel attack by giving the formula of the upper bound of the real secret key rate and comparing it with the lower bound of the secret key rate under Alice and Bob’s estimation. The simulation results quantitatively show the effectiveness of the attack on the imperfect devices at a long distance. Our results emphasize the importance of practical security at the light source and might provide a valuable reference for device selection in the practical implementation of the SNS protocol.

Experimental demonstration of underwater decoy-state quantum key distribution with all-optical transmission.

We demonstrate the underwater quantum key distribution (UWQKD) over a 10.4-meter Jerlov type III seawater channel by building a complete UWQKD system with all-optical transmission of quantum signals, a synchronization signal and a classical communication signal. The wavelength division multiplexing and the space-time-wavelength filtering technology are applied to ensure that the optical signals do not interfere with each other. The system is controlled by FPGA and can be easily integrated into watertight cabins to perform the field experiment. By using the decoy-state BB84 protocol with polarization encoding, we obtain a bit rate of secure keys of 1.82 Kbps and an error rate of 1.55% at the attenuation of 13.26 dB. We prove that the system can tolerate the channel loss up to 23.7 dB and therefore may be used in the 300-meter-long Jerlov type I clean seawater channel.

Evaluation of eavesdropping error-rates in higher-dimensional QKD system implemented using dynamic spatial modes

Secure exchange of cryptographic keys is extremely important for any communication system where security and privacy of data is desirable. Although classical cryptographic algorithms provide computationally secure methods for secret key exchange, quantum key distribution (QKD) provides an extraordinary means to this end by guaranteeing unconditional security. Any malicious interception of communication by a man-in-the-middle on a QKD link immediately alerts sender and receiver by introducing an unavoidable error-rate. Higher-dimensional QKD protocols such as KMB09 exhibit higher eavesdropping error-rates with improved intrusion detection but their practical implementation is still awaited. In this paper, we present the design and implementation of KMB09 protocol using Laguerre–Gaussian orbital angular momentum to demonstrate and highlight the advantages of using dynamic spatial modes in QKD system. A complete error-rate analysis of KMB09 protocol implementation is presented with two different types of eavesdropping error-rates. Furthermore, we also demonstrate the decoy state method to show the robustness of the protocol against photon-number-splitting attack.

Synchronization using quantum photons for satellite-to-ground quantum key distribution.

Time synchronization is crucial for quantum key distribution (QKD) systems. In order to compensate for the time drift caused by the Doppler effect and adapt to the unstable optical link in satellite-to-ground QKD, previous demonstrations generally adopted synchronization methods requiring additional hardware. In this paper, we present a novel synchronization method based on the detected quantum photons, thus simplifying additional hardware and reducing the complexity and cost. This method adopts target frequency scanning to realize fast frequency recovery, utilizes polynomial fitting to compensate for the Doppler effect, and takes use of the vacuum state in the decoy-state BB84 protocol to recover the time offset. This method can avoid the influence of synchronization light jitter, thus improving the synchronization precision and the secure keys as well. Successful satellite-to-ground QKD based on this new synchronization scheme has been conducted to demonstrate its feasibility and performance. The presented scheme provides an effective synchronization solution for quantum communication applications.

A satellite-based quantum key distribution using decoy-state protocol

An ideal QKD implementation that provides the promising unconditional security using single photon laser source is not practically easy, also sending these photons over a fiber channel affects the maximum distance of link up to few hundreds of kilometers because of the receiver’s detectors losses. Therefore, the achievement of a global quantum network is not easy, and the need to use LEO satellites [1,2] for establishing quantum links makes the job easier as quantum free space link provides much less losses to the link than fiber links. Nowadays, a quantum communication link can be established by satellites through free space. in this paper, we propose an implementation [3] of a satellite-based quantum key distribution using decoy-state protocol [4], we then compare this protocol with the BB-84 protocol [3] against security and the key length of the generated shared key.

Security and communication distance improvement in decoy states based quantum key distribution using pseudo-random bases choice for photon polarization measurement

This paper proposes a new quantum key distribution(QKD) protocol, namely the pseudo-random bases entangled photon based QKD (PRB-EPQKD) protocol. The latest mainly focuses on three properties, including the security of the protocol, the secure key size and the maximum communication distance between legitimate communication users (Alice and Bob). To achieve this, we first consider a spontaneous-parametric-down (SPDC) photon source located in a low-earth-orbit (LEO) type satellite capable of producing and distributing entangled photons pairs to Alice and Bob. Secondly, we assume that Alice’s and Bob’s photons state measurement bases are identically generated via a pseudo-random number generator (PRNG), namely the quantum logistic map (QLM). Finally, we also assume that in addition to their photons states, Alice and Bob intentionally share a set of decoy states at each pulse with randomly selected intensity, and with the goal to detect the presence of the eavesdropper (Eve). Under these considerations, the secure key rate upper bound is evaluated applying the Gottesman-Lo-Lutkenhaus-Preskill’s (GLLP) formula, for two different implementations, namely the non-decoy states and the infinite active decoy states based QKD. It is observed a significant improvement in the secure key size and the communication distance as well, compared to existing protocols, since we realize that under daylight, downlinks satellite conditions, a kindly selected light source, and good crystal’s properties, the maximum communication distance can reach up to 70000 km. In addition, using the combined type-I and type-II SPDC photons source as our entangled photons pairs generator, significantly improved the photon mean number and render our protocol more robust against photon number division attack and against attenuation-induced atmospheric propagation. Furthermore, the protocol is more secure as compared to existing ones, given that any eavesdropper must crack simultaneously the chaotic system used as PRNG and the QKD system, before getting any useful information as regards to the measurement bases used by Alice and Bob, and thus the secure key.

Qubit-Based Clock Synchronization for QKD Systems Using a Bayesian Approach.

Quantum key distribution (QKD) systems provide a method for two users to exchange a provably secure key. Synchronizing the users’ clocks is an essential step before a secure key can be distilled. Qubit-based synchronization protocols directly use the transmitted quantum states to achieve synchronization and thus avoid the need for additional classical synchronization hardware. Previous qubit-based synchronization protocols sacrifice secure key either directly or indirectly, and all known qubit-based synchronization protocols do not efficiently use all publicly available information published by the users. Here, we introduce a Bayesian probabilistic algorithm that incorporates all published information to efficiently find the clock offset without sacrificing any secure key. Additionally, the output of the algorithm is a probability, which allows us to quantify our confidence in the synchronization. For demonstration purposes, we present a model system with accompanying simulations of an efficient three-state BB84 prepare-and-measure protocol with decoy states. We use our algorithm to exploit the correlations between Alice’s published basis and mean photon number choices and Bob’s measurement outcomes to probabilistically determine the most likely clock offset. We find that we can achieve a 95 percent synchronization confidence in only 4140 communication bin widths, meaning we can tolerate clock drift approaching 1 part in 4140 in this example when simulating this system with a dark count probability per communication bin width of and a received mean photon number of 0.01.

Bounding passive light-source side channels in quantum key distribution via Hong-Ou-Mandel interference

Passive side-channel attacks in quantum key distribution (QKD) aim at obtaining information about the quantum signals without disturbing them and hence compromise real-world QKD security. Currently, there are no reliable tools for the assessment of QKD signal generation imperfections. In this work we propose a generic experimental method which allows to upper-bound QKD light-source imperfections and directly integrate them into the modern security proofs. The method relies on Hong-Ou-Mandel interference between different emitted signals: the maximum interference visibility reveals overall signal distinguishability that could lead to passive side-channel information leakage. We apply it for the standard decoy-state BB84 protocol and calculate a lower bound on the secret key rate for realistic values of interference visibility. The method can be readily implemented in practical QKD setups and is especially relevant for multiple-laser QKD systems such as the one installed on the Micius satellite.

Explicit attacks on passive side channels of the light source in the BB84 decoy state protocol

Various imperfections of the hardware in quantum key distribution (QKD) lead to discrepancies between the theory and real-world devices. An eavesdropper can use these discrepancies to compromise the QKD security, thus legitimate sides need to estimate the influence of imperfections to prevent the loss of security. Here we investigate explicit eavesdropping attacks on passive side channels of the light source for a BB84 decoy states QKD protocol. We consider an optimal phase-covariant cloning attack, followed by unambiguous state discrimination and a joint measurement. Our calculations provide a hint that for state-of-the-art light sources the inherent presence of passive side channels still allows the protocol to be secure, albeit with the reduced secret key rates.

Passive BB84 decoy-state protocol with a flawed source

Passive generation of quantum states in quantum key distribution (QKD) is an elegant solution to utilise an internal source of quantum randomness of the transmitter’s scheme. It can be profitable, for example, in setups running at high repetition rates. However, the original analysis of passive protocol doesn’t consider real-life effects of a laser source, therefore possibly breaches the unconditional security of the scheme. Here we take into account the influence of various laser imperfections and make a refined comparison between active and passive setups. We show that the new bound on the secret key rate of the passive protocol stays similar to the one of an active scheme, thus proving passive generation to be a practical means of constructing QKD systems.

Loophole-free plug-and-play quantum key distribution

Robust, simple, and flexible quantum key distribution (QKD) is vital for realizing practical applications of this technique. Contrary to typical phase-coded QKD schemes, the plug-and-play QKD design requires only one arm-length-insensitive interferometer without active feedback, in which the noise is automatically compensated by the two-way structure. However, there are certain possible loopholes in the typical plug-and-play designs, which require consideration and strict monitoring. This study proposes a new design of theoretically loophole-free plug-and-play QKD scheme with two-way protocol and presents an experimental demonstration of said scheme. The security is analyzed under a collective attack scenario assisted by the decoy state method. The scheme was implemented in a 50.4 km commercial fibre without active feedback. The system showed highly robust performance with an ultra-low error rate and maintained an ultra-high visibility of 0.9947 ± 0.0002 through significant environmental changes over 24 hours.

Phase-Matching Quantum Key Distribution with Discrete Phase Randomization.

The twin-field quantum key distribution (TF-QKD) protocol and its variations have been proposed to overcome the linear Pirandola–Laurenza–Ottaviani–Banchi (PLOB) bound. One variation called phase-matching QKD (PM-QKD) protocol employs discrete phase randomization and the phase post-compensation technique to improve the key rate quadratically. However, the discrete phase randomization opens a loophole to threaten the actual security. In this paper, we first introduce the unambiguous state discrimination (USD) measurement and the photon-number-splitting (PNS) attack against PM-QKD with imperfect phase randomization. Then, we prove the rigorous security of decoy state PM-QKD with discrete phase randomization. Simulation results show that, considering the intrinsic bit error rate and sifting factor, there is an optimal discrete phase randomization value to guarantee security and performance. Furthermore, as the number of discrete phase randomization increases, the key rate of adopting vacuum and one decoy state approaches infinite decoy states, the key rate between discrete phase randomization and continuous phase randomization is almost the same.

Efficient Verifiable Quantum Secret Sharing Schemes via Eight-Quantum-Entangled States

Quantum secret sharing (QSS) protocols are designed to allow a secret message to be divided into several shadows, and the secret can be reconstructed cooperatively. Motivated by the eight quantum entangled (EQE) state, a tripartite verifiable QSS scheme is proposed. It involves three agents, in four phases, i.e., shadow distribution phase, eavesdropping detection phase, measurement and secret sharing phase, verification and secret recover phase. The protocol can not only share and recover the secret correctly, but also verify whether there are dishonest participants in communication. In addition, the protocol is extended to a multiparty quantum secret sharing scheme by utilizing the unitary operations. Security analysis shows that the proposed schemes achieve the fundamental security requirements against the external and internal attackers with the aid of the quantum decoy states. It is shown that the efficiency in classical and quantum transmission is higher than the other protocols.

Optimizing the decoy-state BB84 QKD protocol parameters

Quantum key distribution (QKD) protocols allow for information theoretically secure distribution of (classical) cryptographic key material. However, due to practical limitations the performance of QKD implementations is somewhat restricted. For this reason, it is crucial to find optimal protocol parameters, while guaranteeing information theoretic security. The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making a number of heuristic assumptions. For instance, the number of decoy states is restricted to only one or two, with one of the decoy intensities set to a fixed value, and vacuum states are ignored as they are assumed to contribute only marginally to the secure key-rate. These assumptions simplify the optimization problem and reduce the size of search space significantly. However, they also cause the security analysis to be non-tight, and thereby result in sub-optimal performance. In this work, we follow a more rigorous approach using both linear and nonlinear programs describing the optimization problem. Our approach, focusing on the decoy-state BB84 protocol, allows heuristic assumptions to be omitted, and therefore results in a tighter security analysis with better protocol parameters. We show an improved performance for the decoy-state BB84 QKD protocol, demonstrating that the heuristic assumptions typically made are too restrictive. Moreover, our improved optimization frameworks shows that the complexity of the performance optimization problem can also be handled without making heuristic assumptions, even with limited computational resources available.

Quantum private comparison of size using d-level Bell states with a semi-honest third party

In this paper, we propose a quantum private comparison $$(\mathrm{QPC})$$ protocol based on Bell states. The presented protocol can determine not only whether two secrets are equal, but also the size relationship between them. The proposed protocol can secretly compare information of the two participants with the help of a third party $$(\mathrm{TP})$$ . The proposed protocol has adopted quantum transmission strategy and the decoy state photons to prevent various types of Eve attacks and participant attacks. It is shown that the protocol is secure in theory.

Improved statistical fluctuation analysis for twin-field quantum key distribution

The decoy state scheme is the most widely studied quantum key distribution protocol to detect existence of eavesdropping. Twin-field quantum key distribution (TF-QKD) is a promising protocol for realizing secret key sharing over long distances. However, the secret key rate becomes relatively low considering the finite-size effect. In this study, the statistical fluctuation analysis of the four-intensity decoy-state TF-QKD system proposed in a recent study (Zhang et al. in Phys Rev A 95:012333, 2017) is considered, and its performance is compared with the results of the Gaussian approximation and Chernoff bound methods. Numerical simulations show that the suggested method shows a considerable improvement in both the key generation rate and transmission distance over the Chernoff bound method under actual experimental environment. We find that the scheme increases secret key rate 1.04–4.06 times and transmission distances 10–18 km farther. We also present optimized parameters for Gaussian, Chernoff, and our scheme.

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.

Experimental decoy-state Bennett-Brassard 1984 quantum key distribution through a turbulent channel

In free-space Quantum Key Distribution in turbulent conditions, scattering and beam wandering cause intensity fluctuations which increase the detected signal-to-noise ratio. This effect can be mitigated by rejecting received bits when the channel's transmittance is below a threshold. Thus, the overall error rate is reduced and the secure key rate increases despite the deletion of bits. In Decoy State BB84 QKD, several methods to find the ideal threshold have already been proposed. One promising method is the Prefixed-Threshold Real-time Selection (P-RTS) where a cutoff can be chosen prior to data collection and independently of the intensity distribution. In this work we perform finite-size Decoy State BB84 QKD in a laboratory setting where we simulate the atmospheric turbulence using an acousto-optical modulator. We show that P-RTS can yield considerably higher secure key rates, especially at higher losses. In addition, we verify that P-RTS gives a robust cutoff even when the predicted transmittance does not match the actual transmittance.

Experimental underwater quantum key distribution.

In recent years, the feasibility of quantum key distribution (QKD) in a water channel has been verified by theory and experiment. Here, we present an experimental investigation of QKD and decoy-state QKD based on the BB84 protocol. The experiment was carried out in a 10 m water tank. The attenuation coefficient of tap water is 0.08/m, which is close to Jerlov Type II seawater. We measured the probability-of-detection matrix of polarization states, and the average fidelity of the four polarization states is up to 98.39%. For the 10 m underwater QKD experiment, 20 MHz optical pulses are generated by modulating the laser diode (LD) and attenuated to an average of 0.1 photons per pulse. The security key rate can reach 563.41 kbits/s and the quantum bit error rate (QBER) is 0.36%. Two decoy states (one of which is the vacuum state) was used in the 10 m underwater decoy-state QKD experiment, and the average QBER of signal state is 0.95%, the security key rate reaches 711.29 kbits/s. According to the parameters of the decoy-state experiment, the maximum secure transmission distance of the underwater decoy-state QKD is predicted to be 19.2 m, while it can be increased to 237.1 m in Jerlov Type I seawater with a lower dark count single photon detector (SPD).

Practical security of wavelength-multiplexed decoy-state quantum key distribution

Wavelength division multiplexing (WDM) of quantum key distribution (QKD) with classical optical channels has been proven to be feasible experimentally. In this paper, we will analyze the practical security of WDM-QKD theoretically. Specifically, we first establish the noise model of classical signals. Then, the influence of classical noises on the performance of decoy-state WDM-QKD is studied with a finite-key security analysis. For numerical simulations, the effect of classical noise-reduction methods for different experimental settings is given. The secret key rate and maximum transmission distance of WDM-QKD is simulated with various sent number of quantum pulses or transmitted power of classical signals. Furthermore, the performance of two kinds of decoy-state WDM-QKD is compared, which shows that the optimal decoy-state protocol for WDM-QKD is related to the sent number of quantum pulses. Since WDM-QKD is desired to reduce the cost of QKD networks and since experiments have already been carried out, our work can not only close the gap between theory and practice, but also be used to optimize the experimental parameters and improve its performance.