Decoy-state Quantum Key Distribution Research Articles

Simplified decoy-state quantum key distribution based on planar lightwave circuit integration module

The BB84 protocol with decoy states for quantum key distribution (QKD) has generated significant interest due to its theoretical unconditional security. Presently, the most of QKD systems demonstrated rely on bulk optics. Nevertheless, in upcoming large-scale commercial availability, it is imperative to have highly integrated, consistently performing, and cost-effective systems. Photonic integrated circuits (PICs) based on silica planar lightwave circuits (PLCs) play a crucial role in QKD due to its mature manufacturing process, excellent stability, low loss, and high integration level. We develop a simplified BB84 time-bin QKD experiment system that can significantly improve the key rate because it does not require time basis decoding. And two silica PLC asymmetric Mach-Zehnder interferometer (AMZI) module are used with a high-precision temperature control system (±0.01 °C). Three quantum states |ψ0⟩, |ψ1⟩ and |ψ+⟩ are encoded and decoded with the module. The system achieves an estimated key rate about 3.4 Mbps using an analytical model with one decoy state at a clock repetition rate of 1.25 GHz. Finally, we experimentally obtain a key rate of 531 kbps over a 20 km single-mode fiber (SMF) at a clock repetition rate of 156.25 MHz.

Improved security bounds against the Trojan-horse attack in decoy-state quantum key distribution

Improved security bounds against the Trojan-horse attack in decoy-state quantum key distribution

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.

Imperfect phase randomization and generalized decoy-state quantum key distribution

Imperfect phase randomization and generalized decoy-state quantum key distribution

Secret key rate bounds for quantum key distribution with faulty active phase randomization

Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization in an active setup, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD when the phase is actively randomized by faulty devices, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.

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.

Reducing the impact of adaptive optics lag on optical and quantum communications rates from rapidly moving sources

Wavefront of light passing through the turbulent atmosphere gets distorted. This causes signal loss in free-space optical communication as the light beam spreads and wanders at the receiving end. Frequency and/or time division multiplexing adaptive optics (AO) techniques have been used to conjugate this kind of wavefront distortion. However, if the signal beam moves relative to the atmosphere, the AO system performance degrades due to high temporal anisoplanatism. Here, we solve this problem by adding a pioneering beacon that is spatially separated from the signal beam with time delay between spatially separated pulses. More importantly, our protocol works irrespective of the signal beam intensity and, hence, is also applicable to secret quantum communication. In particular, using semi-empirical atmospheric turbulence calculation, we show that for low earth orbit satellite-to-ground decoy state quantum key distribution with the satellite at zenith angle <30°, our method increases the key rate by at least 215% and 40% for satellite altitudes of 400 and 800 km, respectively. Finally, we propose a modification of the existing wavelength division multiplexing systems as an effective alternative solution to this problem.

Simplified intensity- and phase-modulated transmitter for modulator-free decoy-state quantum key distribution

Quantum key distribution (QKD) allows secret key exchange between two users with unconditional security. For QKD to be widely deployed, low cost and compactness are crucial requirements alongside high performance. Currently, the majority of QKD systems demonstrated rely on bulk intensity and phase modulators to generate optical pulses with precisely defined amplitude and relative phase difference—i.e., to encode information as signal states and decoy states. However, these modulators are expensive and bulky, thereby limiting the compactness of QKD systems. Here, we present and experimentally demonstrate a novel optical transmitter design to overcome this disadvantage by generating intensity- and phase-tunable pulses at GHz clock speeds. Our design removes the need for bulk modulators by employing directly modulated lasers in combination with optical injection locking and coherent interference. This scheme is, therefore, well suited to miniaturization and photonic integration, and we implement a proof-of-principle QKD demonstration to highlight potential applications.

A fully passive transmitter for decoy-state quantum key distribution

A passive quantum key distribution (QKD) transmitter generates the quantum states prescribed by a QKD protocol at random, combining a fixed quantum mechanism and a post-selection step. By circumventing the use of active optical modulators externally driven by random number generators, passive QKD transmitters offer immunity to modulator side channels and potentially enable higher frequencies of operation. Recently, the first linear optics setup suitable for passive decoy-state QKD has been proposed. In this work, we simplify the prototype and adopt sharply different approaches for BB84 polarization encoding and decoy-state parameter estimation. In particular, our scheme avoids a probabilistic post-selection step that is central to the former proposal. On top of it, we elaborate a simple and tight custom-made security analysis.

Suppression of patterning effect using IQ modulator for high-speed quantum key distribution systems.

Quantum key distribution (QKD) is an attractive technology for distributing secret encryption keys between distant users. The decoy-state technique has drastically improved its practicality and performance, and has been widely adopted in commercial systems. However, conventional intensity modulators can introduce security side channels in high speed QKD systems because of their non-stationary working points for decoy-state generation. Here, we analyze the transfer function of an in-phase/quadrature (IQ) modulator and reveal its superiority for stable decoy-state generation, followed by an experimental demonstration. Thanks to their convenient two-level modulation and inherent high speed, IQ modulators are ideal for use in high-speed decoy-state QKD systems.

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.

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.

Experimental study of secure quantum key distribution with source and detection imperfections

The quantum key distribution (QKD), guaranteed by the principle of quantum physics, is a promising solution for future secure information and communication technology. However, device imperfections compromise the security of real-life QKD systems, restricting the wide deployment of QKD. This study reports a decoy-state BB84 QKD experiment that considers both source and detection imperfections. In particular, we achieved a rigorous finite-key security bound over fiber links of up to 75 km by applying a systematic performance analysis. Furthermore, our study considers more device imperfections than most previous experiments, and the proposed theory can be extended to other discrete-variable QKD systems. These features constitute a crucial step toward securing QKD with imperfect practical devices.

Time scrambling and decoy-state quantum key distribution for optical physical layer encryption

We propose an optical physical layer encryption method based on real-time optical signal temporal scrambling and decoy-state quantum key distribution. The real-time optical signal processing is operating with an array of tunable Fabry-Perot cavities by using the updating and synchronization keys. Based on this scheme, an experimental demonstration is given to realize secure communication for optical physical layer in a standard 10 Gbps data transmission with quantum key distribution in real time. An on-line transmitted data over 100 km of a standard single mode fiber is realized with power penalty of as low as 3.45 dB, where the average key generation rate is better than 800 bps. The experimental results indicate that, the proposed encryption scheme of dynamic scrambling with quantum keys exhibits significantly potential for improving the confidentiality of optical physical layer.

Generation of entangled photons with a second-order nonlinear photonic crystal and a beam splitter

We discuss the generation of entangled photons using a nonlinear photonic crystal and beam splitter. In our method, the photonic crystal is assumed to be composed of a material with a large second-order nonlinear optical susceptibility . Our proposal relies on two facts: (1) A nonlinear photonic crystal changes coherent incident light into squeezed light. (2) A beam splitter transforms the squeezed light into entangled light beams flying in two different directions. We estimate the yield efficiency of pairs of entangled photons per pulse of the very weak coherent light for our method at 0.0783 for a specific concrete example. Our method is more effective because the conversion efficiency (entangled biphotons per incident pump photons) in the spontaneous parametric downconversion is of the order of . The only drawback is that it requires very fine tuning of the frequency of signal photons fed into the photonic crystal; for example, an adjustment is given by Hz for the signal light of Hz. We investigate the application of entangled photons produced by our method to the BB84 quantum key distribution protocol, and we explore how to detect an eavesdropper. We suggest that our method is promising for decoy-state quantum key distribution using weak coherent light.

Finite-Key Analysis of 1-Decoy Method Quantum Key Distribution with Intensity Fluctuation

The decoy state quantum key distribution (QKD) protocol is proven to be an effective strategy against the photon number splitting attack. It was shown that the 1-decoy state protocol, easier to implement in the practical QKD system, outperforms the 2-decoy state protocol for block sizes of up to 108 bits. How intensity fluctuations influence the performance of the 1-decoy state protocol with finite resources remains a pending issue. In this paper, we present a finite-key analysis of the 1-decoy state protocol with intensity fluctuations and obtain the secret key rate formula about intensity fluctuations. Our numerical simulation results show that the stronger the intensity fluctuations, the lower the secret key rate for a small data block size of a few bits. Our research can provide theoretical implications for the selection of data size in the QKD system with intensity fluctuations.

Performance analysis of decoy state quantum key distribution over underwater turbulence channels

Decoy state quantum key distribution protocols have been studied for atmospheric, fiber, and satellite links; however, those results are not directly applicable to underwater environments with different channel characteristics. In this paper, we investigate the fundamental performance limits of decoy state BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. We adopt a near field analysis to determine the average power transfer over a turbulent underwater path and use this to obtain a lower bound on the secret key rate. We quantify the performance of decoy BB84 protocol in different water types assuming various turbulence conditions. We further investigate the effect of system parameters such as transmit aperture size and detector field of view on the performance.