Decoy-state Method Research Articles

Measurement-device-independent quantum random number generation over 23 Mbps with imperfect single-photon sources

Quantum randomness relies heavily on the accurate characterization of the generator implementation, where the device imperfection or inaccurate characterization can lead to incorrect entropy estimation and practical bias, significantly affecting the reliability of the generated randomness. Measurement-device-independent (MDI) quantum random number generation (QRNG) endeavors to produce certified randomness, utilizing uncharacterized and untrusted measurement devices that are vulnerable to numerous attack schemes targeting measurement loopholes. However, existing implementations have shown insufficient performance thus far. Here, we propose a high-speed MDI-QRNG scheme based on a robust measurement tomography approach against the imperfection of single-photon sources. Compared with the conventional approach, the decoy-state method is introduced to obtain more accurate tomography results and a tighter lower bound of randomness. Finally, by using a high-speed time-bin encoding system, we experimentally demonstrated the scheme and obtained a reliable min-entropy lower bound of 7.37×10−2 bits per pulse, corresponding to a generation rate over 23 Mbps, which substantially outperforms the existing realizations and makes a record in discrete-variable semi-device-independent QRNGs.

Experimental high-dimensional quantum key distribution with orbital angular momentum

The development and practical applications of quantum key distribution are limited by the channel capacity and high error rate during long-distance transmission. High-dimensional quantum key distribution protocols solve these problems effectively. In this paper, a high-dimensional quantum key distribution protocol based on polarization-orbit angular momentum is achieved, using a decoy state method to ensure the security of the protocol. The experimental results show that the high-dimensional quantum key distribution protocol improves the encoding efficiency and the upper bound of the quantum bit error rate.

A quantum digital signature protocol with state preparation error tolerance

<sec>The quantum digital signature (QDS) has attracted much attention as it ensures the nonrepudiation, unforgeability, and transferability of signature messages based on information-theoretic security. Amiri et al. (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="https://doi.org/10.1103/PhysRevA.93.032325"><i>Phys. Rev. A</i> <b>93</b> 032325</ext-link>) proposed the first practical QDS protocol based on orthogonal coding, which has realized information-theoretic security and become the mainstream paradigm in QDS research. The procedure of QDS involves two essential stages, the one is the distribution stage, in which Alice-Bob and Alice-Charlie individually utilize the three-intensity decoy-state quantum key distribution protocol but without error correction or privacy amplification, namely, key-generation protocol, to generate correlated bit strings, the other is the messaging stage, in which Alice transmits signature messages to the two recipients.</sec><sec>However, previous theoretical and experimental studies both overlooked the modulation errors that may be introduced in the state preparation process due to the imperfections in modulator devices. Under the traditional framework of GLLP analysis method, these errors will significantly reduce the actual signature rates. Therefore, we propose a state-preparation-error tolerant QDS and use parameter analysis to characterize the state preparation error to make the simulation analysis more realistic. In addition, we analyze the signature rates of the present scheme by using the three-intensity decoy-state method.</sec><sec>Compared with previous QDS protocols, our protocol almost shows no performance degradation under practical state preparation errors and exhibits a maximum transmission distance around 180 km. Furthermore, state preparation errors do not have a significant influence on the bit error rate induced by normal communication between the legitimate users or the one produced by an eavesdropper. These results prove that the method proposed in this paper has excellent robustness against state preparation errors and it can achieve much higher signature rates and signature distances than other standard methods. Besides, signature rates are basically unchanged under different total pulse numbers, which shows that our protocol also has good robustness against the finite-size effect. Additionally, in the key generation process, our method is only required to prepare three quantum states, which will reduce the difficulty of experiment realizations.</sec><sec>Furthermore, the proposed method can also be combined with the measurement-device-independent QDS protocol and the twin-field QDS protocol to further increase the security level of QDS protocol. Therefore, our work will provide an important reference value for realizing the practical application of QDS in the future.</sec>

Security of quantum key distribution with imperfect phase randomisation

The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD.

Decoy-state quantum private query protocol with two-way communication

Quantum private query (QPQ) is a communication protocol established under the condition of mutual distrust between communication parties, which is used to solve the symmetrically private information retrieval problem in the quantum field. However, most of the existing QPQ protocols are based on the ideal light source. In practice, the multi-photon pulse generated by the transmitter will bring great security problems. We analyze the actual security of QPQ protocol in two-way communication, and find that database security and user privacy will be seriously threatened under multi-photon pulse. So we adopt the decoy state method to solve the actual security problem of QPQ protocol in view of the user side as the light source. The results show that the decoy state method is suitable for QPQ protocol of two-way communication, and can effectively defend against multi-photon pulse attacks.

Improved decoy-state quantum key distribution with uncharacterized heralded single-photon sources

Encoding system plays a significant role in quantum key distribution (QKD). However, the security and performance of QKD systems can be compromised by encoding misalignment due to the inevitable defects in realistic devices. To alleviate the influence of misalignments, a method exploiting statistics from mismatched basis is proposed to enable uncharacterized sources to generate secure keys in QKD. In this work, we propose a scheme on four-intensity decoy-state quantum key distribution with uncharacterized heralded single-photon sources. It only requires the source states are prepared in a two-dimensional Hilbert space, and can thus reduce the complexity of practical realizations. Moreover, we carry out corresponding numerical simulations and demonstrate that our present four-intensity decoy-state scheme can achieve a much higher key rate compared than a three-intensity decoy-state method, and meantime it can obtain a longer transmission distance compared than the one using weak coherent sources.

Intensity Tomography Method for Secure and High-Performance Quantum Key Distribution

Decoy-state method has greatly filled in loopholes from multi-photon pulses in the field of quantum key distribution (QKD) and it has been employed in almost all practical QKD systems in recent years. However, security and performance of the practical decoy-state QKDs are still limited by inaccurate modulations such as random intensity fluctuation and correlated intensity fluctuation. In this work, an intensity tomography method is proposed as a countermeasure against these fluctuations. It has an ability to tightly bound the unknown density matrices of photon-number state and accurately calibrate the fluctuations by measuring the decoy states with a local single-photon detector. We verified the tomography method by experiments and simulations. The results indicated that our method can efficiently mitigate the flaws from these fluctuations to improve the protocol performance and practical security. Noting that these fluctuations are inevitable in practical QKDs, our method would pave the avenue for QKD's practical applications.

One-Sided Measurement-Device-Independent Practical Quantum Secure Direct Communication

Measurement-device-independent quantum secure direct communication (MDI-QSDC) protocol is capable of defending against attacks on detectors by illegal parties, and its security relies on the trustworthy preparation of quantum states. In this paper, we propose the one-sided measurement-device-independent quantum secure direct communication (1SMDI-QSDC) protocol, which not only has the advantage of being independent of detection loopholes but also weakens the requirement of MDI-QSDC for state preparation. We analyze the real-life secrecy capacity of this proposed protocol by using realistic experimental settings that contain the weak coherent pulse source, parametric down-conversion source, and customized decoy-state method. The results indicate that our protocols can achieve secure communication over a few hundred kilometers. Furthermore, we find that the coding technology of increasing capacity using masking (INCUM) can mitigate the degradation of the maximum distance of secure communication when the state preparation is highly untrustworthy.

Overcoming Fundamental Bounds on Quantum Conference Key Agreement

Twin-Field Quantum Key Distribution (TF-QKD) enables two distant parties to establish a shared secret key, by interfering weak coherent pulses (WCPs) in an intermediate measuring station. This allows TF-QKD to reach greater distances than traditional QKD schemes and makes it the only scheme capable of beating the repeaterless bound on the bipartite private capacity. Here, we generalize TF-QKD to the multipartite scenario. Specifically, we propose a practical conference key agreement (CKA) protocol that only uses WCPs and linear optics and prove its security with a multiparty decoy-state method. Our protocol allows an arbitrary number of parties to establish a secret conference key by single-photon interference, enabling it to overcome recent bounds on the rate at which conference keys can be established in quantum networks without a repeater.

Optical transmitter for time-bin encoding quantum key distribution

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

Patterning-Effect Calibration Algorithm for Secure Decoy-State Quantum Key Distribution

The decoy-state method for the quantum key distribution (QKD) is a great countermeasure against the fatal photon number splitting attack. At present, the decoy-state method has been widely employed in practical QKD systems. However, the patterning effect, namely the correlated intensity fluctuations in practical QKD systems, violates the important assumption of the decoy-state method and seriously threatens the protocol security. The previous works investigated the patterning effect between the adjacent pulses and proposed the countermeasures from the degree of post selection and modulators. In this work, we investigate the patterning effect with larger correlation range and present an algorithm to calibrate the driving voltages to mitigate the patterning effect. According to our methods, we experimentally observe the higher-order patterning effect and successfully mitigate it by our calibration algorithm. The experiment results indicate that our methods efficiently improve the protocol security and are expected to be widely employed in practical decoy-state QKD systems.

Analysis of an injection-locking-loophole attack from an external source for quantum key distribution

Many security loopholes exist in quantum key distribution (QKD) due to the imperfections of realistic devices. On the source side, the decoy-state method can defend against the most severe photon-number-splitting (PNS) attack and improve the performance of QKD. Measurement-device-independent QKD and twin-field QKD have further closed all loopholes on the detection side. In this paper, we propose a valuable optical injection-locking loophole for the case when the internal isolator inside the laser is removed. We first introduce the effects of the injection locking with different injection intensities on the source frequency. Through the successive responses of adjacent pulses from frequency ports of the dense wavelength division multiplexer, the decoy state and the signal state can be partially distinguished. The specific injection-locking-loophole analysis of the isolatorless decoy phase-encoding Bennet-Brassard 1984 QKD and decoy phase-matching QKD protocols with external optical injection has been deeply studied. Simulation results show that, if we maintain the same observed gain statistics as normal after an external optical injection locking, the loophole cannot be exploited for a PNS attack when the QKD distance is short. As the QKD distance increases, a PNS attack at a medium distance using the optical injection-locking loophole does not threaten the security; the security is still valid. With the further increase of the QKD distance, the lower-bound secure key rate is higher than the upper-bound secure key rate given by a PNS attack at a long distance, some of the keys must be insecure, and information will be leaked.

Security of Decoy-State Quantum Key Distribution with Correlated Intensity Fluctuations

One of the most prominent techniques to enhance the performance of practical quantum key distribution (QKD) systems with laser sources is the decoy-state method. Current decoy-state QKD setups operate at gigahertz repetition rates, a regime where memory effects in the modulators and electronics that control them create correlations between the intensities of the emitted pulses. This translates into information leakage about the selected intensities, which cripples a crucial premise of the decoy-state method, thus invalidating the use of standard security analyzes. To overcome this problem, a security proof that exploits the Cauchy-Schwarz constraint has been introduced recently. Its main drawback is, however, that the achievable key rate is significantly lower than that of the ideal scenario without intensity correlations. Here, we improve this security proof technique by combining it with a fine-grained decoy-state analysis, which can deliver a tight estimation of the relevant parameters that determine the secret key rate. This results in a notable performance enhancement, being now the attainable distance double that of previous analyzes for certain parameter regimes. Also, we show that when the probability density function of the intensity fluctuations, conditioned on the current and previous intensity choices, is known, our approach provides a key rate very similar to the ideal scenario, which highlights the importance of an accurate experimental characterization of the correlations.

Detecting the possibility of a type of photon number splitting attack in decoy-state quantum key distribution

The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate the secure key rate, while it still considers that only single-photon pulses can generate secure keys in any case. However, multiphoton pulses can also generate secure keys if we can detect the possibility of PNS attack in the channel. The ultimate goal of this line of research is to confirm the absence of all types of PNS attacks. In particular, the PNS attack mentioned and detected in this paper is only the weaker version of PNS attack which significantly changes the observed values of the legitimate users. In this paper, under the null hypothesis of no weaker version of PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state protocols, extract a Cauchy distribution statistic, and further provide a detection method and the type I error probability. If the result is judged to be an attack, we can use the existing decoy-state method and the GLLP formula to estimate the secure key rate. Otherwise, the pulses with the same basis received including both single-photon pulses and multiphoton pulses, can be used to generate the keys and we give the secure key rate in this case. Finally, the associated experiments we performed (i.e., the significance level is 5%) show the correctness of our method.

Security analysis for a mutually partially unbiased bases–based protocol

The recently proposed mutually partially unbiased bases (MPUB)–based protocol, which encodes with Laguerre–Gaussian modes and Hermite–Gaussian modes of the same mode order, can close the security loophole caused by state-dependent diffraction. However, its pessimistic security proof limits the performance, and some practical issues, such as finite-key size and imperfect sources, have not been considered. Here, we improve the key rates of the MPUB-based protocol by accurately estimating the phase error rate. Moreover, the effect of finite-key size and its performance when combined with the decoy state method are demonstrated. Our work broadens the application scope of the MPUB-based protocol, and thereby advances the development of high-dimensional quantum key distribution using spatial modes.

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing.

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user’s pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method.

Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case

Detection-efficiency mismatch is a common problem in practical quantum key distribution (QKD) systems. Current security proofs of QKD with detection-efficiency mismatch rely either on the assumption of the single-photon light source on the sender side or on the assumption of the single-photon input of the receiver side. These assumptions impose restrictions on the class of possible eavesdropping strategies. Here we present a rigorous security proof without these assumptions and, thus, solve this important problem and prove the security of QKD with detection-efficiency mismatch against general attacks (in the asymptotic regime). In particular, we adapt the decoy state method to the case of detection-efficiency mismatch.

Sending-or-Not-Sending Twin-Field Quantum Key Distribution with a Passive Decoy-State Method

Twin-field quantum key distribution (TF-QKD) has attracted considerable attention because it can exceed the basic rate-distance limit without quantum repeaters. Its variant protocol, sending or not-sending quantum key distribution (SNS-QKD), not only fixes the security vulnerability of TF-QKD, but also can tolerate large misalignment errors. However, the current SNS-QKD protocol is based on the active decoy-state method, which may lead to side channel information leakage when multiple light intensities are modulated in practice. In this work, we propose a passive decoy-state SNS-QKD protocol to further enhance the security of SNS-QKD. Numerical simulation results show that the protocol not only improves the security in source, but also retains the advantages of tolerating large misalignment errors. Therefore, it may provide further guidance for the practical application of SNS-QKD.

Passive decoy state phase matching quantum key distribution

In this paper, a passive decoy state phase matching quantum key distribution scheme is proposed based on the heralded pair coherent state light source to make the protocol more practical and safe. Without changing the intensity of the light source, we can derive four different data sets by dividing the raw key data into four groups according to the combined results of detectors in source end. The scheme can make use of the different data sets to estimate the parameters and extract the secret key. The key generation rate formula is derived after the parameter estimation. The performance of the proposed scheme is analyzed with and without taking statistical fluctuation into consideration. The simulation results show that compared with the existing active decoy-state method, the proposed passive method has slightly lower key rate when the transmission distance is short, and has obviously higher key rate when the transmission distance exceeds 406[Formula: see text]km. The maximum safety transmission distance of the proposed scheme is 452[Formula: see text]km which is relatively further. According to the influence of statistical fluctuation, the performance of the proposed scheme declines as the length of the data falls. Even though the data size is [Formula: see text], the max safety transmission distance is also more than 400[Formula: see text]km.

Practical Security of High-Dimensional Quantum Key Distribution with Intensity Modulator Extinction.

Quantum key distribution (QKD) has attracted much attention due to its unconditional security. High-dimensional quantum key distribution (HD-QKD) is a brand-new type of QKD protocol that has many excellent advantages. Nonetheless, practical imperfections in realistic devices that are not considered in the theoretical security proof may have an impact on the practical security of realistic HD-QKD systems. In this paper, we research the influence of a realistic intensity modulator on the practical security of HD-QKD systems with the decoy-state method and finite-key effects. We demonstrate that there is a certain impact in the secret key rate and the transmission distance when taking practical factors into security analysis.