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Chinese Physics B

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

Yuan Li, Wan‐Su Bao, Hong-Wei Li, Chun Hua Zhou, Yang Wang

Published Nov 1, 2015• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1674-1056/24/11/110307

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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.
Passive decoy-state quantum key distribution (QKD) systems, proven to be more desirable than the active ones in some scenarios, also have the problem of device imperfections like intensity fluctuations. In this paper, the formula of key generation rate of the passive decoy-state protocol using the weak coherent pulse (WCP) source with intensity fluctuation is given, and then the influence of intensity fluctuations on the performance of the passive decoy-state protocol is rigorously characterized. From numerical simulations, it can be seen that intensity fluctuations have non-negligible influence on the performance of the passive decoy-state QKD protocol with WCP source. Most importantly, our simulations show that, under the same deviation of intensity fluctuations, the passive decoy-state method performs better than the active one decoy-state method and is close to the active vacuum + weak decoy-state method.
Decoy states have recently been proposed as a useful protocol for substantially improving the performance of quantum key distribution (QKD). The passive decoy-state protocol has the advantage of easier implementation, higher transmission rate and better security compared with the active decoy-state protocol. This paper analyzes the passive decoy-state protocol with different light sources, including the lastest passive state protocol with weak coherent state (WCS) and the simple passive state protocol (AYKI) with heralded single photon source (HSPS). Based on the theoretic discussion and numerical simulation, we obtain the conclusion that the passive decoy-state protocol with HSPS is easier to implement than the passive decoy-state protocol with WCS because the latter need a hardware change but the former dose not involve any hardware change on the statnard QKD scheme. The key generation rate of the passive decoy-state protocol with WCS is better than that of the passive decoy-state protocol with HSPS, but the transmission distance is less than the latter. Anyhow, the performance of the passive scheme with a threshold detector is close to the active one.
Passive decoy-state quantum key distribution systems, proven to be more desirable than active ones in some scenarios, also have the problem of device imperfections like finite-length keys. In this paper, based on the WCP source which can be used for the passive decoy-state method, we obtain the expressions of single-photon error rates, single-photon counts, and phase error rates. According to the information of smooth min-entropy, we calculate the key generation rate under the condition of finite-length key. Key generation rates with different numbers of pulses are compared by numerical simulations. From the results, it can be seen that the passive decoy-state method can have good results if the total number of pulses reaches 10 10 . We also simulate the passive decoy-state method with different probabilities of choosing a pulse for parameter estimation when the number of pulses is fixed.
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.
A nonorthogonal passive decoy-state method is presented with a reconstructive weak coherent state source. The method dose not prepare decoy states actively and divides the receiver detection events into two groups, i.e., triggered components and nontriggered components, according to triggering situation of the sender detector. Both triggered and nontriggered components, as signal states and decoy states, are used to do some estimations and to generate secure key. The simulation results show that a better key generation rate and a longer secure transmission distance can be obtained with the nonorthogonal passive decoy-state method than with the existing passive methods, and that the performance is comparable to the theoretical limit of an active infinite decoy-state protocol. Furthermore, the nontriggered component contribution to key generation offsets the limitation of the detector low efficiency, and the performance of the method dose not depend on the detector efficiency of sender. Because decoy states need not be prepared actively, and our protocol is easy to implement and apply to quantum key distribution at high transmission rates.
The passive decoy scheme represents a quantum key distribution protocol that employs a photon number resolving detector to selectively extract the decoy states from the signal states during post-processing. This selection process ensures resilience against attacks capable of distinguishing between these two states, thereby enhancing the security of the protocol. Previous research has emphasized the good performance of the protocol under optimal conditions. However, our study focuses on numerically evaluating the protocol performance in various practical scenarios. We aim to understand the implications of these scenarios in terms of the maximum attainable attenuation and bit rate per second, considering the number of photons per pulse sent under specific experimental conditions. Our findings demonstrate that opting for a low average photon number value ensures high tolerance to attenuation during communication, albeit at the cost of a reduced bit rate per second. Conversely, for lower attenuations, it is more advantageous to increase the average number of photons, even if it deviates from the ideal behaviour of a single-photon source. The benefit of selecting the decoy states at the end of the transmission remains consistent across different configurations. This research signifies an advancement in assessing the viability of incorporating the protocol within a practical QKD network.