Decoy-state Research Articles

Adaptive spatial filtering of daytime sky noise in a satellite quantum key distribution downlink receiver

Spatial filtering is an important technique for reducing sky background noise in a satellite quantum key distribution downlink receiver. Atmospheric turbulence limits the extent to which spatial filtering can reduce sky noise without introducing signal losses. Using atmospheric propagation and compensation simulations, the potential benefit of adaptive optics (AO) to secure key generation (SKG) is quantified. Simulations are performed assuming optical propagation from a low-Earth-orbit satellite to a terrestrial receiver that includes AO. Higher-order AO correction is modeled assuming a Shack–Hartmann wavefront sensor and a continuous-face-sheet deformable mirror. The effects of atmospheric turbulence, tracking, and higher-order AO on the photon capture efficiency are simulated using statistical representations of turbulence and a time-domain wave-optics hardware emulator. SKG rates are calculated for a decoy-state protocol as a function of the receiver field of view for various strengths of turbulence, sky radiances, and pointing angles. The results show that at fields of view smaller than those discussed by others, AO technologies can enhance SKG rates in daylight and enable SKG where it would otherwise be prohibited as a consequence of background optical noise and signal loss due to propagation and turbulence effects.

Secure polarization-independent subcarrier quantum key distribution in optical fiber channel using BB84 protocol with a strong reference.

A quantum key distribution system based on the subcarrier wave modulation method has been demonstrated which employs the BB84 protocol with a strong reference to generate secure bits at a rate of 16.5 kbit/s with an error of 0.5% over an optical channel of 10 dB loss, and 18 bits/s with an error of 0.75% over 25 dB of channel loss. To the best of our knowledge, these results represent the highest channel loss reported for secure quantum key distribution using the subcarrier wave approach. A passive unidirectional scheme has been used to compensate for the polarization dependence of the phase modulators in the receiver module, which resulted in a high visibility of 98.8%. The system is thus fully insensitive to polarization fluctuations and robust to environmental changes, making the approach promising for use in optical telecommunication networks. Further improvements in secure key rate and transmission distance can be achieved by implementing the decoy states protocol or by optimizing the mean photon number used in line with experimental parameters.

Heralded single-photon sources for quantum-key-distribution applications

Single photon sources (SPS) are a fundamental building block for optical implementations of quantum information protocols. Among SPSs, multiple crystal heralded single photon sources seem to give the best compromise between high pair production rate and low multiple photon events. In this work, we study their performance in a practical quantum key distribution experiment, by evaluating the achievable key rates. The analysis focuses on the two different schemes, symmetric and asymmetric, proposed for the practical implementation of heralded single photon sources, with attention on the performance of their composing elements. The analysis is based on the protocol proposed by Bennett and Brassard in 1984 and on its improvement exploiting decoy state technique. Finally, a simple way of exploiting the post-selection mechanism for a passive, one decoy state scheme is evaluated.

Experimental comparison between one-decoy and two-decoy implementations of the Bennett-Brassard 1984 quantum cryptography protocol

The decoy-state method allows the use of weak coherent pulses in quantum cryptography, and to date, various strategies for the decoy state have been proposed. Here, we experimentally compare the secret key generation rates between the one-decoy and two-decoy implementations of the Bennett-Brassard 1984 (BB84) quantum key distribution protocol through a 3.1-km optical fiber at 780 nm. Once the parameters of the experimental setup are optimized for the maximal secret key generation rate for each implementation, it is found that the two-decoy implementation outperforms the one-decoy implementation.

Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions

Nonorthogonal coded agreements and decoy state method can effectively protect the photon number against splitting attack. Owing to the fact that the component of single-photon in the coherent-state superposition (CSS) is as high as 90%, CSS has recently emerged as an alternative to single-photon qubits for quantum information processing and metrology. The approximate CSS of small amplitudes is generated by the subtraction of photons from a squeezed vacuum state, and the approximate CSS of large amplitude is generated from Fock state by using a single homodyne detection. Here, we combine both of the methods and propose a new protocol by using the CSS as a light source. We derive the secure key generation rate, the lower bound of count rate and upper bound of error rate of single-photon. We simulate the curves relationship between secure key generation rate and safety transmission distance in the case of an infinite number of decoy states by using matlab. The parameters are given according to the Gobby-Yuan-Shields (GYS) experiment. We infer that the safety transmission distance achieves 147.4 km and the secure key generation rate is much higher than those of other schemes. We also simulate the relationship between key generation rate and safety transmission distance in the case of a limited number of decoy states by using matlab. The parameters are given according to the GYS experiment too. When the N is 1010, the safety transmission distance achieves 144 km; when the N is 109, the safety transmission distance achieves 139 km; when the N is 108, the safety transmission distance achieves 125.9 km. In this paper, we propose the use of CSS as the light source. Combining SARG04 agreements and decoy state, the scheme has the following advantages: first, the scheme which combines SARG04 agreements and decoy state method can effectively resist PNS; second, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions has a longer safety transmission distance and higher secure key generation rate than nonorthogonal decoy-state quantum key distribution based on weak coherent pulse and nonorthogonal decoy-state quantum key distribution based on conditionally prepared down-conversion source; third, nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions is easier to prepare, which just needs one decoy state, than other schemes that require several decoy states. Obviously, our scheme can enhance the performance of quantum key distribution. Nonorthogonal decoy-state quantum key distribution based on coherent-state superpositions will have a very good application with the further development of preparation technology of CSS.

Optimal mean photon number of decoy state protocol based on chameleon self-adaptive strategy under the background of rainfall

As one of the most common weathers in daily life, the rain can change the atmospheric compositions and humidity in a short time, which may cause non-ignorable attenuation in free-space quantum communication system. Besides, the absorption and scattering effects caused by raindrops can also bring huge attenuation to photon's propagation. In order to solve this burst interference caused by rain weather, optimal mean photon number per pulse and chameleon self-adaptive algorithm (CSA) are proposed based on the rainfall distribution model and decoy-state quantum key distribution. Due to the lack of producing mature ideal single photon source technology, the decoy-state protocol with highly attenuated laser becomes the most practical and most widely used quantum secure communication protocol currently. Among all the different kinds of decoy-state protocols, the vacuum+weak decoy state quantum communication secure protocol is chosen to be the basis of our research. Besides, in order to study the influence of mean photon number per signal pulse, we set the pulse ratio between signal state, decoy state and vacuum state to be fixed at 2:2:1. Since the performance of the vacuum+weak decoy state quantum communication system is closely related to the mean photon number per pulse, it is very necessary to confirm the optimal value. Combining the Weibull rainfall distribution model and Mie scattering theory, we first analyze the attenuation caused by rainfall in a free-space quantum communication system. Then the functional relationship among opt, rainfall intensity (J) and link distance (L) is built by studying the propagation of highly attenuated laser in depolarizing channel. Finally, two parameters, secure key rate and channel survival function, are chosen to evaluate the system's performance of reliability and validity. These two parameters are respectively compared between the system with and without CSA. Simulation results show that, as J=30 mm/24 h, L=30 km, the secure key generation rate rises from 210-4 up to 3.510-4 when using the CSA in the quantum communication system; as J=60 mm/24 h, L=20 km, the quantum channel survival function value increases from 0.52 to 0.63; as the quantum channel survival function value is required no lower than 0.5, the rainfall intensity in which quantum communication system can survive rises from 62 mm/24 h up to 74 mm/24 h. These results prove that there is a close relationship between opt and the channel parameters of the quantum communication system under the background of rainfall. Therefore, it is necessary for us to self-adapt the opt value by combining rainfall intensity with the CSA strategy if the reliability and survivability of free space quantum communication system are required to be improved.

Using Modeling and Simulation to Study Photon Number Splitting Attacks

Quantum key distribution (QKD) is an innovative technology, which exploits the laws of quantum mechanics to generate and distribute unconditionally secure shared cryptographic keying material between two geographically separated parties. The unique nature of QKD that ensures eavesdropping on the key distribution channel necessarily introduces detectable errors and shows promise for high-security environments, such as banking, government, and military. However, QKD systems are vulnerable to advanced theoretical and experimental attacks. In this paper, the photon number splitting (PNS) attack is studied in a specialized QKD modeling and simulation framework. First, a detailed treatment of the PNS attack is provided with emphasis on practical considerations, such as performance limitations and realistic sources of error. Second, ideal and non-ideal variations of the PNS attack are studied to measure the eavesdropper’s information gain on the QKD-generated secret key bits and examine the detectability of PNS attacks with respect to both quantum bit error rate and the decoy state protocol. Finally, this paper provides a repeatable methodology for efficiently studying advanced attacks, both realized and notional, against QKD systems and more generally quantum communication protocols.

Implementation Of Decoy State Protocol

We report the experimental demonstration of decoy state QKD using commercial QKD system based on a standard bi-directional 'Plug & Play' set-up. By making simple modifications to a commercial quantum key distribution system, decoy state QKD allows us to achieve much better performance than QKD system without decoy state in terms of key generation rate and distance. We demonstrate an unconditionally secure key rate of 9.7008 × 10-4 per pulse for a 25 km fiber length

Statistical-fluctuation analysis for quantum key distribution with consideration of after-pulse contributions

Statistical fluctuation problems are faced by all quantum key distribution (QKD) protocols under finite-key condition. Most of the current statistical fluctuation analysis methods work based on independent random samples, however, the precondition cannot be always satisfied on account of different choice of samples and actual parameters. As a result, proper statistical fluctuation methods are required to figure out this problem. Taking the after-pulse contributions into consideration, we give the expression of secure key rate and the mathematical model for statistical fluctuations, focusing on a decoy-state QKD protocol (Sci Rep. 3, 2453, 2013) with biased basis choice. On this basis, a classified analysis of statistical fluctuation is represented according to the mutual relationship between random samples. First for independent identical relations, we make a deviation comparison between law of large numbers and standard error analysis. Secondly, we give a sufficient condition that Chernoff bound achieves a better result than Hoeffding's inequality based on independent relations only. Thirdly, by constructing the proper martingale, for the first time we represent a stringent way to deal with statistical fluctuation issues upon dependent ones through making use of Azuma's inequality. In numerical optimization, we show the impact on secure key rate, the ones and respective deviations under various kinds of statistical fluctuation analyses.

Experimental quantum key distribution with simulated ground-to-satellite photon losses and processing limitations

Quantum key distribution (QKD) has the potential to improve communications security by offering cryptographic keys whose security relies on the fundamental properties of quantum physics. The use of a trusted quantum receiver on an orbiting satellite is the most practical near-term solution to the challenge of achieving long-distance (global-scale) QKD, currently limited to a few hundred kilometers on the ground. This scenario presents unique challenges, such as high photon losses and restricted classical data transmission and processing power due to the limitations of a typical satellite platform. Here we demonstrate the feasibility of such a system by implementing a QKD protocol, with optical transmission and full post-processing, in the high-loss regime using minimized computing hardware at the receiver. Employing weak coherent pulses with decoy states, we demonstrate the production of secure key bits at up to 56.5 dB of photon loss. We further illustrate the feasibility of a satellite uplink by generating secure key while experimentally emulating the varying channel losses predicted for realistic low-Earth-orbit satellite passes at 600 km altitude. With a 76 MHz source and including finite-size analysis, we extract 3374 bits of secure key from the best pass. We also illustrate the potential benefit of combining multiple passes together: while one suboptimal "upper-quartile" pass produces no finite-sized key with our source, the combination of three such passes allows us to extract 165 bits of secure key. Alternatively, we find that by increasing the signal rate to 300 MHz it would be possible to extract 21570 bits of secure finite-sized key in just a single upper-quartile pass.

Getting something out of nothing in the measurement-device-independent quantum key distribution

Because of the monogamy of entanglement, the measurement-device-independent quantum key distribution is immune to the side-information leaking of the measurement devices. When the correlated measurement outcomes are generated from the dark counts, no entanglement is actually obtained. However, secure key bits can still be proven to be generated from these measurement outcomes. Especially, we will give numerical studies on the contributions of dark counts to the key generation rate in practical decoy state MDI-QKD where a signal source, a weaker decoy source and a vacuum decoy source are used by either legitimate key distributer.

Free-space measurement-device-independent quantum-key-distribution protocol using decoy states with orbital angular momentum**Project supported by the National Natural Science Foundation of China (Grant Nos. 61271238 and 61475075), the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20123223110003), the Natural Science Research Foundation for Universities of Jiangsu Province of China (Grant No. 11KJA510002), the Open Research Fund

In this paper, we propose a measurement-device-independent quantum-key-distribution (MDI-QKD) protocol using orbital angular momentum (OAM) in free space links, named the OAM-MDI-QKD protocol. In the proposed protocol, the OAM states of photons, instead of polarization states, are used as the information carriers to avoid the reference frame alignment, the decoy-state is adopted to overcome the security loophole caused by the weak coherent pulse source, and the high efficient OAM-sorter is adopted as the measurement tool for Charlie to obtain the output OAM state. Here, Charlie may be an untrusted third party. The results show that the authorized users, Alice and Bob, could distill a secret key with Charlie’s successful measurements, and the key generation performance is slightly better than that of the polarization-based MDI-QKD protocol in the two-dimensional OAM cases. Simultaneously, Alice and Bob can reduce the number of flipping the bits in the secure key distillation. It is indicated that a higher key generation rate performance could be obtained by a high dimensional OAM-MDI-QKD protocol because of the unlimited degree of freedom on OAM states. Moreover, the results show that the key generation rate and the transmission distance will decrease as the growth of the strength of atmospheric turbulence (AT) and the link attenuation. In addition, the decoy states used in the proposed protocol can get a considerable good performance without the need for an ideal source.

Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.

In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation.

Passive decoy-state quantum key distribution using weak coherent pulses with modulator attenuation**Project supported by the National Natural Science Foundation of China (Grant No. 11304397).

Passive decoy-state quantum key distribution is more desirable than the active one in some scenarios. It is also affected by the imperfections of the devices. In this paper, the influence of modulator attenuation on the passive decoy-state method is considered. We introduce and analyze the unbalanced Mach–Zehnder interferometer, briefly, and combining with the virtual source and imaginary unitary transformation, we characterize the passive decoy-state method using a weak coherent photon source with modulator attenuation. According to the attenuation parameter δ, the pass efficiencies are given. Then, the key generation rate can be acquired. From numerical simulations, it can be seen that modulator attenuation has a nonnegligible influence on the performance of passive-state QKD protocol. Based on the research, the analysis method of virtual source and imaginary unitary transformation are preferred in analyzing passive decoy state protocol, and the passive decoy-state method is better than the active one and is close to the active vacuum + weak decoy state under the condition of having the same modulator attenuation.

Quantum key distribution: examination of the decoy state protocol

Quantum key distribution (QKD) is an innovative technology that exploits the laws of quantum mechanics to generate and distribute a shared cryptographic key for secure communications. The unique nature of QKD ensures that eavesdropping on quantum communications necessarily introduces detectable errors which is desirable for high-security environments. QKD systems have been demonstrated in both freespace and optical fiber configurations, gaining global interest from national laboratories, commercial entities, and the U.S. Department of Defense. However, QKD is a nascent technology where realized systems are constructed from non-ideal components, which can significantly impact system performance and security. In this article, we describe QKD technology as part of a secure communications solution and identify vulnerabilities associated with practical network architectures. In particular, we examine the performance of decoy state enabled QKD systems against a modeled photon number splitting attack and suggest an improvement to the decoy state protocol security condition that does not assume a priori knowledge of the QKD channel efficiency.

Quantum key distribution over 120 km using ultrahigh purity single-photon source and superconducting single-photon detectors.

Advances in single-photon sources (SPSs) and single-photon detectors (SPDs) promise unique applications in the field of quantum information technology. In this paper, we report long-distance quantum key distribution (QKD) by using state-of-the-art devices: a quantum-dot SPS (QD SPS) emitting a photon in the telecom band of 1.5 μm and a superconducting nanowire SPD (SNSPD). At the distance of 100 km, we obtained the maximal secure key rate of 27.6 bps without using decoy states, which is at least threefold larger than the rate obtained in the previously reported 50-km-long QKD experiment. We also succeeded in transmitting secure keys at the rate of 0.307 bps over 120 km. This is the longest QKD distance yet reported by using known true SPSs. The ultralow multiphoton emissions of our SPS and ultralow dark count of the SNSPD contributed to this result. The experimental results demonstrate the potential applicability of QD SPSs to practical telecom QKD networks.

Decoy-state measurement-device-independent quantum key distribution with mismatched-basis statistics

Measurement-device-independent quantum key distribution (MDI-QKD) is aimed at removing all detector side channel attacks, while its security relies on the assumption that the encoding systems including sources are fully characterized by the two legitimate parties. By exploiting the mismatched-basis statistics in the security analysis, MDI-QKD even with uncharacterized qubits can generate secret keys. In this paper, considering the finite size effect, we study the decoy-state MDI-QKD protocol with mismatched-basis events statistics by performing full parameter optimization, and the simulation result shows that this scheme is very practical.

Finite-key security analysis of quantum key distribution with imperfect light sources

In recent years, the gap between theory and practice in quantum key distribution (QKD) has been significantly narrowed, particularly for QKD systems with arbitrarily flawed optical receivers. The status for QKD systems with imperfect light sources is however less satisfactory, in the sense that the resulting secure key rates are often overly dependent on the quality of state preparation. This is especially the case when the channel loss is high. Very recently, to overcome this limitation, Tamaki et al proposed a QKD protocol based on the so-called ‘rejected data analysis’, and showed that its security—in the limit of infinitely long keys—is almost independent of any encoding flaw in the qubit space, being this protocol compatible with the decoy state method. Here, as a step towards practical QKD, we show that a similar conclusion is reached in the finite-key regime, even when the intensity of the light source is unstable. More concretely, we derive security bounds for a wide class of realistic light sources and show that the bounds are also efficient in the presence of high channel loss. Our results strongly suggest the feasibility of long distance provably secure communication with imperfect light sources.

Approaching the ideal quantum key distribution with two-intensity decoy states

Approaching the ideal quantum key distribution with two-intensity decoy states

A new scheme on improving the performance of the quantum key distribution with two-intensity weak coherent light

In this paper, we propose a new scheme on implementing the quantum key distribution with two-intensity weak coherent light and compare its performance with other existing methods. Through numerical simulations, we demonstrate that our new scheme can exceed almost all other existing decoy-state methods, e.g., the standard three-intensity decoy-state method and the usual passive decoy-state method, both in the transmission distance and in the final key generation rate, approaching very closely to the ideal case of using an infinite number of decoy states. Besides, we also consider the finite-size key effect. We demonstrate that under current experimental conditions, even when taking statistical fluctuation into account, a quite high key generation rate can still be obtained at very long transmission distance by applying our new scheme.