In the decoy quantum key distribution, we show that a smaller decoy intensity gives a better key generation rate in the asymptotic setting when we employ only one decoy intensity and the vacuum pulse. In particular, the counting rate of single photon can be perfectly estimated when the decoy intensity is infinitesimal. The same property holds even when the intensities cannot be perfectly identified. Further, we propose a protocol to improve the key generation rate over the existing protocol under the same decoy intensity.
Passive decoy-state quantum key distribution (QKD) systems, proven to be more desirable than active ones in some scenarios, also have the problem of device imperfections like intensity fluctuations. In this paper the formular of key generation rate of the passive decoy-state protocol using transformed weak coherent pulse (WCP) source with intensity fluctuation is given, and then the influence of intensity fluctuations on the performance of passive decoy-state protocol is rigorously characterized. From numerical simulations, it can be easily seen that intensity fluctuations have unignorable inf…
We propose an efficient four-intensity decoy-state BB84 protocol and derive concise security bounds for this protocol with the universally composable finite-key analysis method. Comparing with the efficient three-intensity protocol, we find that our efficient four-intensity protocol can increase the secret key rate by at least $30\%$. Particularly, this increasing rate of secret key rate will be raised as the transmission distance increases. At a large transmission distance, our efficient four-intensity protocol can improve the performance of quantum key distribution profoundly.
We present a general theorem for the efficient verification of the lower bound of single-photon transmittance. We show how to do decoy-state quantum key distribution efficiently with large random errors in the intensity control. In our protocol, the linear terms of fluctuation disappear and only the quadratic terms take effect. We then show the unconditional security of decoy-state method with whatever error pattern in intensities of decoy pulses and signal pulses provided that the intensity of each decoy pulse is less than $μ$ and the intensity of each signal pulse is larger than $μ'$.
Quantum key distribution (QKD) is a technology that allows two users to exchange keys securely. The decoy state technique enhances the technology, ensuring keys can be shared at high bit rates over long distances with information theoretic security. However, imperfections in the implementation, known as side-channels, threaten the perfect security of practical QKD protocols. Intensity modulators are required for high-rate decoy state QKD systems, although these are unstable and can display a side channel where the intensity of a pulse is dependent on the previous pulse. Here we demonstrate the…
The decoy-state method has been developed rapidly in quantum key distribution (QKD) since it is immune to photon-number splitting attacks. However, two basis detector efficiency asymmetry, which exists in realistic scenarios, has been ignored in the prior results. By using the recent 4-intensity decoy-state optimization protocol, we report the first implementation of high-rate QKD with asymmetric basis detector efficiency, demonstrating 1.9 to 33.2 times higher key rate than previous protocols in the situation of large basis detector efficiency asymmetry. The results ruled out an implicitly as…
We present improved results and more general results for the decoy-state measurement device independent quantum key distribution (MDI-QKD) where the intensities of all 3 pulses can be non-zero. We present a more tightened explicit formula for the lower bound of the yield of two single-photon pulses for this generalized 3-intensity protocol, which can be applied to the recently proposed MDI-QKD with imperfect single-photon sources such as the coherent states or the heralded states from the parametric down-conversion. We strictly prove that our result is better than the prior art result. With th…
We present an improved statistical fluctuation analysis for measurement device independent quantum key distribution with three-intensity decoy-state method. Taking the statistical fluctuations for different sources jointly, we present more tightened formulas for some key quantities used in calculating the secure final key. Numerical simulation shows that, given the total number of pulses $10^{12}$, our method improves the key rate by about 97\% for a distance of 50kms compared with the result given by Xu., et al. (Phys. Rev. A 89, 052333); and improves the key rate by $146\%$ for a distance of…
The decoy-state high-dimensional quantum key distribution provides a practical secure way to share more private information with high photon-information efficiency. In this paper, based on detector-decoy method, we propose a detector-decoy high-dimensional quantum key distribution protocol. Employing threshold detectors and a variable attenuator, we can estimate single-photon fraction of postselected events and Eves Holevo information under the Gaussian collective attack with much simpler operations in practical implementation. By numerical evaluation, we show that without varying source inten…
We study the measurement device independent quantum key distribution (MDI-QKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method. We present a more tightened explicit formula to estimate the lower bound of the yield of two-single-photon pulses. Moreover, we show that the bounding of this yield and phase flip error of single photon pulse pairs can be further improved by using other constraints which can be solved by a simple and explicit program. Results of numerical simulation for key rates with both the improved explicit formula a…
Decoy State Quantum Key Distribution (QKD), being capable of beating PNS attack and uncon- ditionally secure, have become an attractive one recently. But, in many QKD systems, disturbances of transmission channel make quantum bit error rate (QBER) increase which limits both security distance and key bit rate of real-life decoy state QKD systems. We demonstrate the two-intensity decoy QKD with one-way Faraday-Michelson phase modulation system, which is free of channel dis- turbance and keeps interference fringe visibility (99%) long period, near 130KM single mode optical fiber in telecom (1550 …
Measurement-device-independent quantum key distribution (MDI-QKD) with weak coherent sources has been widely and meticulously analyzed. However, the analysis for MDI-QKD with spontaneous parametric-down-conversion sources (SPDCS) is incomplete. In this paper, by accounting for practical parameters of SPDCS with thermal distribution, we presents an investigation on the performances of MDI-QKD under the active three-intensity decoy protocol and the passive one-intensity decoy protocol respectively. Phase randomization, inherently prerequisite for decoy protocol, is taken into consideration for e…
We study the measurement device independent quantum key distribution (MDIQKD) in practice with limited resource, when there are only 3 different states in implementing the decoy-state method and when there are basis dependent coding errors. We present general formulas for the decoy-state method for two-pulse sources with 3 different states, which can be applied to the recently proposed MDIQKD with imperfect single-photon source such as the coherent states or the heralded states from the parametric down conversion. We point out that the existing result for secure QKD with source coding errors d…
It has been shown that in the asymptotic case of infinite-key length the 2-decoy state QKD protocol outperforms the 1-decoy state protocol. Here, we present a finite-key analysis of the 1-decoy method. Interestingly, we find that for practical block sizes of up to $10^8$ bits, the 1-decoy protocol achieves for almost all experimental settings higher secret key rates than the 2-decoy protocol. Since using only one decoy is also easier to implement, we conclude that it is the best choice for practical QKD.
Twin-Field (TF) quantum key distribution (QKD) represents a novel QKD approach whose principal merit is to beat the point-to-point private capacity of a lossy quantum channel, thanks to performing single-photon interference in an untrusted node. Indeed, recent security proofs of various TF-QKD type protocols have confirmed that the secret key rate of these schemes scales essentially as the square root of the transmittance of the channel. Here, we focus on the TF-QKD protocol introduced by Curty et al, whose secret key rate is nearly an order of magnitude higher than previous solutions. Its sec…
We show the unconditional security of decoy-state method quantum cryptography with whatever intensity error pattern provided that the error is not too large. Our result immediately applies to the existing experimental data. Our result is not limitted to coherent states.
Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution. Here, we present a general theory of the decoy state protocol based on only two decoy states and one signal state. We perform optimization on the choice of intensities of the two decoy states and the signal state. Our result shows that a decoy state protocol with only two types of decoy states--the vacuum and a weak decoy state--asymptotically approaches the theoretical limit of the most general type of decoy state protocols (with an infinite number of decoy stat…
In this paper, security of practically decoy state quantum key distribution under fake state attack is considered. If quantum key distribution is insecure under this type of attack, decoy sources can not also provide it with enough security. Strictly analysis shows that Eve should eavesdrop with the aid of photon-number-resolving instruments. In practical implementation of decoy state quantum key distribution where statistical fluctuation is considered, however, Eve can attack it successfully with threshold detectors.
Experimental one-way decoy pulse quantum key distribution running continuously for 60 hours is demonstrated over a fiber distance of 20km. We employ a decoy protocol which involves one weak decoy pulse and a vacuum pulse. The obtained secret key rate is on average over 10kbps. This is the highest rate reported using this decoy protocol over this fiber distance and duration.
Decoy state method closes source security loophole in quantum key distribution (QKD) using laser source. In this method, accurate estimates of the detection rates of vacuum and single photon events plus the error rate of single photon events are needed to give a good enough lower bound of the secret key rate. Nonetheless, the current estimation method for these detection and error rates, which uses three types of photon intensities, is accurate up to about 1% relative error. Here I report an experimentally feasible way that greatly improves these estimates and hence increases the one-way key r…
We present relevant bounds for the case of weak+vacuum decoy state and one decoy state for a two way four states Quantum Key Distribution (QKD) protocol. The numerical simulation result was significant given that an improvement in maximum secure distance of nearly double is achieved.
For quantum key distribution (QKD) using spontaneous parametric-down-conversion sources (SPDCSs), the passive decoy-state protocol has been proved to be efficiently close to the theoretical limit of an infinite decoy-state protocol. In this paper, we apply a tight finite-key analysis for the passive decoy-state QKD using SPDCSs. Combining the security bound based on the uncertainty principle with the passive decoy-state protocol, a concise and stringent formula for calculating the key generation rate for QKD using SPDCSs is presented. The simulation shows that the secure distance under our for…
We show how to calculate the fraction of single photon counts of the 3-intensity decoy-state quantum cryptography faithfully with both statistical fluctuations and source errors. Our results only rely on the bound values of a few parameters of the states of pulses.
The method of decoy-state quantum key distribution (QKD) requests different intensities of light pulses. Existing theory has assumed exact control of intensities. Here we propose a simple protocol which is secure and efficient even there are errors in intensity control. In our protocol, decoy pulses and signal pulses are generated from the same father pulses with a two-value attenuation. Given the upper bound of fluctuation of the father pulses, our protocol is secure provided that the two-value attenuation is done exactly. We propose to use unbalanced beam-splitters for a stable attenuation. …
High-dimensional quantum key distribution (HD-QKD) allows two parties to generate multiple secure bits of information per detected photon. In this work, we show that decoy state protocols can be practically implemented for HD-QKD using only one or two decoy states. HD-QKD with two decoy states, under realistic experimental constraints, can generate multiple secure bits per coincidence at distances over 200 km and at rates similar to those achieved by a protocol with infinite decoy states. Furthermore, HD-QKD with only one decoy state is practical at short distances, where it is almost as secur…
The decoy-state method is widely used in practical quantum key distribution systems to replace ideal single photon sources with realistic light sources by varying intensities. Instead of active modulation, the passive decoy-state method employs built-in decoy states in a parametric down-conversion photon source, which can decrease the side channel information leakage in decoy state preparation and hence increase the security. By employing low dark count up-conversion single photon detectors, we have experimentally demonstrated the passive decoy-state method over a 50-km-long optical fiber and …
Twin-field quantum key distribution (TF-QKD), which is immune to all possible detector side channel attacks, enables two remote legitimate users to perform secure communications without quantum repeaters. With the help of a central node, TF-QKD is expected to overcome the linear key-rate constraint using current technologies. However, the security of the former TF-QKD protocols relies on the hypothesis of infinite-key and stable sources. In this paper, we present the finite-key analysis of a practical decoy-state twin-field quantum key distribution with variant statistical fluctuation models. …
To increase dramatically the distance and the secure key generation rate of quantum key distribution (QKD), the idea of quantum decoys--signals of different intensities--has recently been proposed. Here, we present the first experimental implementation of decoy state QKD. By making simple modifications to a commercial quantum key distribution system, we show that a secure key generation rate of 165bit/s, which is 1/4 of the theoretical limit, can be obtained over 15km of a Telecom fiber. We also show that with the same experimental parameters, not even a single bit of secure key can be extract…
We report on the first demonstration of a two way Quantum Key Distribution protocol with decoy state. The experiment was conducted over free space medium and exhibits a significant increase in the maximum secure distance.
Without actively aligning the reference frames, the reference-frame-independent quantum key distribution (RFI-QKD) can generate secure keys even when the reference frames drift slowly. Here, we propose a new scheme on the decoy-state RFI-QKD, where the basis assignments of two legitimate parties are biased, reducing the fraction of mismatched-basis data. When accounting for statistical fluctuations under different misalignments of reference frames, we investigate the performance of biased decoy-state RFI-QKD with full parameter optimization. We also make a clear comparison between the new sche…
To beat PNS attack, decoy state quantum key distribution (QKD) based on coherent state has been studied widely. We present a decoy state QKD protocol with modified coherent state (MCS). By destruction quantum interference, MCS with fewer multi-photon events can be get, which may improve key bit rate and security distance of QKD. Through numerical simulation, we show about 2-dB increment on security distance for BB84 protocol.
We study the possible application of the decoy state method on a basic two way quantum key distribution (QKD) scheme to extend its distance. Noting the obvious advantage of such a QKD scheme in allowing for single as well as double photon contributions, we derive relevant lower-bounds on the corresponding gains in a practical decoy state implementation using two intensities for decoy states. We work with two different approaches in this vein and compare these with an ideal infinite decoy state case as well as the simulation of the original.
Decoy state protocols are a useful tool for many quantum key distribution systems implemented with weak coherent pulses, allowing significantly better secret bit rates and longer maximum distances. In this paper we present a method to numerically find optimal three-level protocols, and we examine how the secret bit rate and the optimized parameters are dependent on various system properties, such as session length, transmission loss, and visibility. Additionally, we show how to modify the decoy state analysis to handle partially distinguishable decoy states as well as uncertainty in the prepar…
The relatively low key rate seems to be the major barrier to its practical use for the decoy state measurement device independent quantum key distribution (MDIQKD). We present a 4-intensity protocol for the decoy-state MDIQKD that hugely raises the key rate, especially in the case the total data size is not large. Also, calculation shows that our method makes it possible for secure private communication with {\em fresh} keys generated from MDIQKD with a delay time of only a few seconds.
Decoy-state quantum key distribution (QKD) has become the most efficient method to resist the photon-number-splitting (PNS) attack and estimate the secure key rate. The decoy-state method has many assumptions, among which a critical one is that an eavesdropper (Eve) cannot distinguish between the signal and decoy states. However, a rigorous proof of the rationality about this assumption is not yet available so far. In fact, due to the difference of photon-number probability distribution between the signal and decoy states, Eve is able to distinguish the two states with a certain probability. I…
In this paper, a new decoy-state scheme for quantum key distribution with parametric down-conversion source is proposed. We use both three-intensity decoy states and their triggered and nontriggered components to estimate the fraction of single-photon counts and quantum bit-error rate of single-photon, and then deduce a more accurate value of key generation rate. The final key rate over transmission distance is simulated, which shows that we can obtain a higher key rate than that of the existing methods, including our own earlier work.
We develop a general theory for quantum key distribution (QKD) in both the forward error correction and the reverse error correction cases when the QKD system is equipped with phase-randomized coherent light with arbitrary number of decoy intensities. For this purpose, generalizing Wang's expansion, we derive a convex expansion of the phase-randomized coherent state. We also numerically check that the asymptotic key generation rates are almost saturated when the number of decoy intensities is three.
This paper provides a formula for the sacrifice bit-length for privacy amplification with the Bennett-Brassard 1984 protocol for finite key lengths when we employ the decoy method. Using the formula, we can guarantee the security parameter for realizable quantum key distribution system. The key generation rates with finite key lengths are numerically evaluated. The proposed method improves the existing key generation rate even in the asymptotic setting.
Decoy state method quantum key distribution (QKD) is one of the promising practical solutions to BB84 QKD with coherent light pulses. In the real world, however, statistical fluctuations with the finite code length cannot be negligible, and the securities of theoretical and experimental researches of the decoy method state QKD so far are based on the asymptotic GLLP's formula which guarantees only that the limit of eavesdropper's information becomes zero as the code length approaches infinity. In this paper, we propose a substantially improved decoy state QKD in the framework of the finite cod…
In practical quantum key distribution (QKD), weak coherent states as the photon sources have a limit in secure key rate and transmission distance because of the existence of multiphoton pulses and heavy loss in transmission line. Decoy states method and nonorthogonal encoding protocol are two important weapons to combat these effects. Here, we combine these two methods and propose a efficient method that can substantially improve the performance of QKD. We find a 79 km increase in transmission distance over the prior record using decoy states method.
Recently, Hwang has proposed a decoy state method in quantum key distribution (QKD). In Hwang's proposal, the average photon number of the decoy state is about two. Here, we propose a new decoy state scheme using vacua or very weak coherent states as decoy states and discuss its advantages.
Twin-Field quantum key distribution (TF-QKD) and its variants, e.g. Phase-Matching QKD, Sending-or-not-sending QKD, and No Phase Post-Selection TFQKD promise high key rates at long distance to beat the rate distance limit without a repeater. The security proof of these protocols are based on decoy-state method, which is usually performed by actively modulating a variable optical attenuator together with a random number generator in practical experiments, however, active-decoy schemes like this may lead to side channel and could open a security loophole. To enhance the source security of TF-QKD…
Measurement-device-independent quantum key distribution (MDI-QKD) has been demonstrated in both laboratories and field-tests using attenuated lasers combined with the decoy-state technique. Although researchers have studied various decoy-state MDI-QKD protocols with two or three decoy states, a clear comparison between these protocols is still missing. This invokes the question of how many types of decoy states are needed for practical MDI-QKD. Moreover, the system parameters to implement decoy-state MDI-QKD are only partially optimized in all previous works, which casts doubt on the actual pe…
We propose a practical decoy state method with heralded single photon source for quantum key distribution (QKD). In the protocol, 3 intensities are used and one can estimate the fraction of single-photon counts. The final key rate over transmission distance is simulated under various parameter sets. Due to the lower dark count than that of a coherent state, it is shown that a 3-intensity decoy-state QKD with a heralded source can work for a longer distance than that of a coherent state.
Quantum key distribution establishes a secret string of bits between two distant parties. Of concern in weak laser pulse schemes is the especially strong photon number splitting attack by an eavesdropper, but the decoy state method can detect this attack with current technology, yielding a high rate of secret bits. In this Letter, we develop rigorous security statements in the case of finite statistics with only a few decoy states, and we present the results of simulations of an experimental setup of a decoy state protocol that can be simply realized with current technology.
Decoy states have recently been proposed as a useful method for substantially improving the performance of quantum key distribution protocols when a coherent state source is used. Previously, data post-processing schemes based on one-way classical communications were considered for use with decoy states. In this paper, we develop two data post-processing schemes for the decoy-state method using two-way classical communications. Our numerical simulation (using parameters from a specific QKD experiment as an example) results show that our scheme is able to extend the maximal secure distance from…
We report here a complete experimental realization of one-way decoy-pulse quantum key distribution, demonstrating an unconditionally secure key rate of 5.51 kbps for a 25.3 km fibre length. This is two orders of magnitudes higher than the value that can be obtained with a non-decoy system. We introduce also a simple test for detecting the photon number splitting attack and highlight that it is essential for the security of the technique to fully characterize the source and detectors used.
We propose the improved decoy state quantum key distribution incorporating finite statistics due to the finite code length and report on its demonstration. In our experiment, four different intensities including the vacuum state for optimal pulses are used and the key generation rate of 200 bps is achieved in the 20 km telecom optical fiber transmission keeping the eavesdropper's mutual information with the final key less than 2^{-9}.
We present a method without decoy state to estimate faithfully and efficiently the yield and quantum bit error rate of single photon pulse for BB84 protocol. The numerical calculations show that key generation rate and maximal secure communication distance of our method are better than results of the decoy state method. As we know, it is the first time we present this method and the idea is very novel. Furthermore, our method can overcome the drawbacks of decoy state method. In our method, the maximal secure distance is insensitive to the deviation of dark count rate from exact value.
Decoy state quantum key distribution (QKD) has been proposed as a novel approach to improve dramatically both the security and the performance of practical QKD set-ups. Recently, many theoretical efforts have been made on this topic and have theoretically predicted the high performance of decoy method. However, the gap between theory and experiment remains open. In this paper, we report the first experiments on decoy state QKD, thus bridging the gap. Two protocols of decoy state QKD are implemented: one-decoy protocol over 15km of standard telecom fiber, and weak+vacuum protocol over 60km of s…
Decoy state method could effectively enhance the performance of quantum key distribution (QKD) with practical phase randomized weak coherent source. Although active modulation of the source intensity is effective and has been implemented in many experiments, passive preparation of decoy states is also an important addition to the family of decoy state QKD protocols. In this paper, following the theory of Curty \emph{et al.} [PRA, 81, 022310 (2010)], we experimentally demonstrate the phase-encoding passive-decoy-state QKD with only linear optical setups and threshold single photon detectors. In…
We analyse the finite-size security of the efficient Bennett-Brassard 1984 protocol implemented with decoy states and apply the results to a gigahertz-clocked quantum key distribution system. Despite the enhanced security level, the obtained secure key rates are the highest reported so far at all fibre distances.
Measurement-device-independent quantum key distribution (MDI-QKD) is immune to all the detection attacks; thus when it is combined with the decoy-state method, the final key is unconditionally secure, even if a practical weak coherent source is used by Alice and Bob. However, until now, the analysis of decoy-state MDI-QKD with a weak coherent source is incomplete. In this paper, we derive, with only vacuum+weak decoy state, some tight formulas to estimate the lower bound of yield and the upper bound of error rate for the fraction of signals in which both Alice and Bob send a single-photon puls…
We propose a method to prepare different non-Poissonian signal pulses from sources of Poissonian photon number distribution using only linear optical elements and threshold photon detectors. This method allows a simple passive preparation of decoy states for quantum key distribution. We show that the resulting key rates are comparable to the performance of active choices of intensities of Poissonian signals.
