Effect of weak randomness flaws on security evaluation of practical quantum key distribution with distinguishable decoy states

Quantum key distribution provides an unconditional secure key sharing method in theory,but the imperfect factors of practical devices will bring security vulnerabilities.In this paper,we characterize the imperfections of the sender and analyze the possible attack strategies of Eve.Firstly,we present a quantized model for distinguishability of decoy states caused by intensity modulation.Besides,considering that Eve may control the preparation of states through hidden variables,we evaluate the security of preparation in practical quantum key distribution(QKD)scheme based on the weak-randomness model.Finally,we analyze the influence of the distinguishability of decoy state to secure key rate,for Eve may conduct the beam splitting attack and control the channel attenuation of different parts.Through the simulation,it can be seen that the secure key rate is sensitive to the distinguishability of decoy state and weak randomness,especially when Eve can control the channel attenuation.

Practical non-orthogonal decoy state quantum key distribution with heralded single photon source

Recently the performance of the quantum key distribution （QKD） is substantially improved by the decoy state method and the non-orthogonal encoding protocol, separately. In this paper, a practical non-orthogonal decoy state protocol with a heralded single photon source （HSPS） for QKD is presented. The protocol is based on 4 states with different intensities. i.e. one signal state and three decoy states. The signal state is for generating keys; the decoy states are for detecting the eavesdropping and estimating the fraction of single-photon and two-photon pulses. We have discussed three cases of this protocol, i.e. the general case, the optimal case and the special case. Moreover, the final key rate over transmission distance is simulated. For the low dark count of the HSPS and the utilization of the two-photon pulses, our protocol has a higher key rate and a longer transmission distance than any other decoy state protocol.

Free-space measurement-device-independent quantum-key-distribution protocol using decoy states with orbital angular momentum

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.

Decoy State Quantum Key Distribution via Beam-Wandering Modeled Atmosphere Channel

We investigate the decoy state quantum key distribution via the atmosphere channels. We consider the efficient decoy state method with one-signal state and two-decoy states. Our results show that the decoy state method works even in the channels with fluctuating transmittance. Nevertheless, the key generation rate will be dra-matically decreased by atmosphere turbulence, which sheds more light on the characterization of atmosphere turbulence in realistic free-space based quantum key distributions.

Security of the Decoy State Two-Way Quantum Key Distribution with Finite Resources

The quantum key distribution （QKD） allows two parties to share a secret key by typically making use of a one-way quantum channel. Howevery the two-way QKD has its own unique advantages, which means the two-way QKD has become a focus recently. To improve the practieM performance of the two-way QKD, we present a security analysis of a two-way QKD protocol based on the decoy method with heralded single-photon sources （HSPSs）. We make use of two approaches to calculate the yield and the quantum bit error rate of single-photon and two-photon pulses. Then we present the secret key generation rate based on the GLLP formula. The numerical simulation shows that the protocol with HSPSs has an advantage in the secure distance compared with weak coherent state sources. In addition, we present the final secret key by considering the statistical fluctuation of the yield generation rate of the LM05 protocol with finite resources and the error rate.

One-decoy state reference-frame-independent quantum key distribution

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

Experimental demonstration of passive decoy state quantum key distribution

Passive decoy state quantum key distribution（PDS-QKD） has advantages in high-speed scenarios.We propose a modified model to simulate the PDS-QKD with a weak coherent light source based on Curty＇s theory [Opt.Lett.34 3238（2009）].The modified model can provide better performance in a practical PDS-QKD system.Moreover,we report an experimental demonstration of the PDS-QKD of over 22.0-dB channel loss.

Improved statistical fluctuation analysis for two decoy-states phase-matching quantum key distribution

Phase-matching quantum key distribution is a promising scheme for remote quantum key distribution,breaking through the traditional linear key-rate bound.In practical applications,finite data size can cause significant system performance to deteriorate when data size is below 1010.In this work,an improved statistical fluctuation analysis method is applied for the first time to two decoy-states phase-matching quantum key distribution,offering a new insight and potential solutions for improving the key generation rate and the maximum transmission distance while maintaining security.Moreover,we also compare the influence of the proposed improved statistical fluctuation analysis method on system performance with those of the Gaussian approximation and Chernoff-Hoeffding boundary methods on system performance.The simulation results show that the proposed scheme significantly improves the key generation rate and maximum transmission distance in comparison with the Chernoff-Hoeffding approach,and approach the results obtained when the Gaussian approximation is employed.At the same time,the proposed scheme retains the same security level as the Chernoff-Hoeffding method,and is even more secure than the Gaussian approximation.

Practical decoy-state BB84 quantum key distribution with quantum memory

We generalize BB84 quantum key distribution(QKD) to the scenario where the receiver adopts a heralded quantum memory(QM). With the heralded QM, the valid dark count rate of the receiver's single photon detectors can be mitigated obviously, which will lower the quantum bit error rate, and thus improve the performance of decoy-state BB84 QKD systems in long distance range. Simulation results show that, with practical experimental system parameters, decoy-state BB84 QKD with QM can exhibit performance comparable to that of without QM in short distance range, and exhibit performance better than that without QM in long distance range.

Passive decoy-state quantum key distribution using weak coherent pulses with modulator attenuation

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 6, 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 non- negligible 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.

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.

A long-distance quantum key distribution scheme based on pre-detection of optical pulse with auxiliary state

We construct a circuit based on PBS and CNOT gates, which can be used to determine whether the input pulse is empty or not according to the detection result of the auxiliary state, while the input state will not be changed. The circuit can be treated as a pre-detection device. Equipping the pre-detection device in the front of the receiver of the quantum key distribution （QKD） can reduce the influence of the dark count of the detector, hence increasing the secure communication distance significantly. Simulation results show that the secure communication distance can reach 516 km and 479 km for QKD with perfect single photon source and decoy-state QKD with weak coherent photon source, respectively.

New protocols for non-orthogonal quantum key distribution

Combining the passive decoy-state idea with the active decoy-state idea, a non-orthogonal （SARG04） decoy-state protocol with one vacuum and two weak decoy states is introduced based on a heralded pair coherent state photon source for quantum key distribution. Two special cases of this protocol are deduced, i.e., a one-vacuum-and-one-weak-decoy-state protocol and a one-weak-decoy-state protocol. In these protocols, the sender prepares decoy states actively, which avoids the crude estimation of parameters in the SARG04 passive decoy-state method. With the passive decoy-state idea, the detection events on Bob＇s side that are non-triggered on Alice＇s side are not discarded, but used to estimate the fractions of single-photon and two-photon pulses, which offsets the limitation of the detector＇s low efficiency and overcomes the shortcoming that the performance of the active decoy-state protocol critically depends on the efficiency of detector. The simulation results show that the combination of the active and passive decoy-state ideas increases the key generation rate. With a one-vacuum-and-two-weak-decoy-state protocol, one can achieve a key generation rate that is close to the theoretical limit of an infinite decoy-state protocol. The performance of the other two protocols is a little less than with the former, but the implementation is easier. Under the same condition of implementation, higher key rates can be obtained with our protocols than with existing methods.

Decoy-state method for quantum-key-distribution-based quantum private query

The quantum private query(QPQ)is a quantum solution for the symmetrically private information retrieval problem.We study the security of quantum-key-distribution-based QPQ with weak coherent pulses.The result shows that multiphoton pulses have posed a serious threat to the participant’s privacy in QPQ protocols.Then we propose a decoy-state method that can help the honest participant detect the attack by exploiting multiphoton pulses and improving the key distillation process to defend against such attack.The analysis demonstrates that our decoy-state method significantly improves the security of the QPQ with weak coherent pulses,which solves a major obstacle in the practical application of the QPQ.

Performance of passive decoy-state quantum key distribution with mismatched local detectors

In quantum key distribution(QKD),the passive decoy-state method can simplify the intensity modulation and reduce some of side-channel information leakage and modulation errors.It is usually implemented with a heralded single-photon source.In Wang et al 2016(Phys.Rev.A 96032312),a novel passive decoy-state method is proposed by Wang et al,which uses two local detectors to generate more detection events for tightly estimating channel parameters.However,in the original scheme,the two local detectors are assumed to be identical,including the same detection efficiency and dark count rate,which is often not satisfied in the realistic experiment.In this paper,we construct a model for this passive decoy-state QKD scheme with two mismatched detectors and explore the effect on QKD performance with certain parameters.We also take the finite-size effect into consideration,showing the performance with statistical fluctuations.The results show that the efficiencies of local detectors affect the key rate more obviously than dark count rates.