Photon-number-solving Decoy State Quantum Key Distribution
Qing-yu Cai, Yong-gang Tan
备注：
This is a detailed and extended version of quant-ph/0504221. In this paper, a detailed discussion of photon-number-resolving QKD scheme is presented. Moreover, the detailed discussion of coherent multiphoton pulse attack (CMP) is presented. 2 figures and some discussions are added. A detailed cauculation of the "new" upper bound 'is presented
In this paper, a photon-number-resolving decoy state quantum key distribution scheme is presented based on recent experimental advancements. A new upper bound on the fraction of counts caused by multiphoton pulses is given. This upper bound is independent of intensity of the decoy source, so that both the signal pulses and the decoy pulses can be used to generate the raw key after verified the security of the communication. This upper bound is also the lower bound on the fraction of counts caused by multiphoton pulses as long as faint coherent sources and high lossy channels are used. We show that Eve's coherent multiphoton pulse (CMP) attack is more efficient than symmetric individual (SI) attack when quantum bit error rate is small, so that CMP attack should be considered to ensure the security of the final key. finally, optimal intensity of laser source is presented which provides 23.9 km increase in the transmission distance. 03.67.Dd
We analyze the security of the efficient two-party quantum private comparison protocol with decoy photons and two-photon entanglement. It is shown that the compromised third party (TP) can obtain the final comparison result without introducing any detectable errors in the standard semi-honest model. The attack strategy is discussed in detail and an improvement of this protocol is demonstrated. The idea of our attack might be instructive for the cryptanalysis of quantum cryptographic schemes.
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.
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 present a scheme for multiparty quantum secret sharing of a private key with pure entangled states and decoy photons. The boss, say Alice uses the decoy photons, which are randomly in one of the four nonorthogonal single-photon states, to prevent a potentially dishonest agent from eavesdropping freely. This scheme requires the parties of communication to have neither an ideal single-photon quantum source nor a maximally entangled one, which makes this scheme more convenient than others in a practical application. Moreover, it has the advantage of having high intrinsic efficiency for qubits …
The decoy-state method is a standard enhancement to quantum key distribution (QKD) protocols that has enabled countless QKD experiments with inexpensive light sources. However, new technological advancements might require further theoretical study of this technique. In particular, the decoy-state method is typically described under the assumption of a Poisson statistical distribution for the number of photons in each QKD pulse. This is a practical choice, because prepare-and-measure QKD is often implemented with attenuated lasers, which produce exactly this distribution. However, sources that …
Decoy-state protocols provide a way to defeat photon-number splitting attacks in quantum cryptography implemented with weak coherent pulses. We point out that previous security analyses of such protocols relied on assumptions about eavesdropping attacks that considered treating each pulse equally and independently. We give an example to demonstrate that, without such assumptions, the security parameters of previous decoy-state implementations could be worse than the ones claimed. Next we consider more general photon-number splitting attacks, which correlate different pulses, and give an estima…
We report on a bright, nondegenerate type-I parametric down-conversion source, which is well suited for passive decoy-state quantum key distribution. We show the photon-number-resolved analysis over a broad range of pump powers and we prove heralded higher-order $n$-photon states up to $n=4$. The inferred photon click statistics exhibit excellent agreements to the theoretical predictions. From our measurement results we conclude that our source meets the requirements to avert photon-number-splitting attacks.
A quantum secure direct communication network scheme is proposed with quantum superdense coding and decoy photons. The servers on a passive optical network prepare and measure the quantum signal, i.e., a sequence of the $d$-dimensional Bell states. After confirming the security of the photons received from the receiver, the sender codes his secret message on them directly. For preventing a dishonest server from eavesdropping, some decoy photons prepared by measuring one photon in the Bell states are used to replace some original photons. One of the users on the network can communicate any othe…
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 …
We demonstrate the decoy-state quantum key distribution over 200 km with photon polarization through optical fiber, by using super-conducting single photon detector with a repetition rate of 320 Mega Hz and a dark count rate of lower than 1 Hz. Since we have used the polarization coding, the synchronization pulses can be run in a low frequency. The final key rate is 14.1 Hz. The experiment lasts for 3089 seconds with 43555 total final bits.
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…
Quantum Key Distribution (QKD) is an innovative quantum communications protocol which exploits the laws of quantum mechanics to generate unconditionally secure cryptographic keying material between two geographically separated parties. The unique nature of QKD shows promise for high-security applications such as those found in banking, government, and military environments. However, QKD systems contain implementation non-idealities which can negatively impact their performance and security.In particular, QKD systems often employ the decoy state protocol to improve system throughput and mitigat…
The round-robin differential phase-shift quantum key distribution protocol provides a secure way to exchange private information without monitoring conventional disturbances and still maintains a high tolerance of noise, making it desirable for practical implementations of quantum key distribution. However, photon number resolving detectors are required to ensure that the detected signals are single photons in the original protocol. Here, we adopt the detector-decoy method and give the bounds to the fraction of detected events from single photons. Utilizing the advantages of the protocol, we p…
Quantum key distribution with decoherence-free subspaces has been proposed to overcome the collective noise to the polarization modes of photons flying in quantum channel. Prototype of this scheme have also been achieved with parametric-down conversion source. However, a novel type of photon-number-splitting attack we proposed in this paper will make the practical implementations of this scheme insecure since the parametric-down conversion source may emit multi-photon pairs occasionally. We propose decoy states method to make these implementations immune to this attack. And with this decoy sta…
Parametric down-conversion (PDC) sources can be used for quantum key distribution (QKD). One can use a PDC source as a triggered single photon source. Recently, there are various practical proposals of the decoy state QKD with triggering PDC sources. In this paper, we generalize the passive decoy state idea, originally proposed by Mauerer and Silberhorn. The generalized passive decoy state idea can be applied to cases where either threshold detectors or photon number resolving detectors are used. The decoy state protocol proposed by Adachi, Yamamoto, Koashi and Imoto (AYKI) can be treated as a…
We investigate the use of photon number states to identify eavesdropping attacks on quantum key distribution (QKD) schemes. The technique is based on the fact that different photon numbers traverse a channel with different transmittivity. We then describe two QKD schemes that utilize this method, one of which overcomes the upper limit on the key generation rate imposed by the dead time of detectors when using a heralded source of photons.
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.
In this paper, we describe a robust quantum cryptography scheme with a heralded single photon source based on the decoy-state method, which has been shown by numerical simulations to be advantageous compared with many other practical schemes not only with respect to the secure key generation rate but also to secure transmission distance. We have experimentally tested this scheme, and the results support the conclusions from numerical simulations well. Although there still exist many deficiencies in our present systems, it's still sufficient to demonstrate the advantages of the scheme. Besides,…
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 study the decoy-state measurement-device-independent quantum key distribution using heralded single-photon sources. This has the advantage that the observed error rate in X basis is in higher order and not so large. We calculate the key rate and transmission distance for two cases: one using only triggered events, and the other using both triggered and non-triggered events. We compare the key rates of various protocols and find that our new scheme using triggered and non-triggered events can give higher key rate and longer secure distance. Moreover, we also show the different behavior of ou…
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.
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 propose a decoy-state method to overcome the photon-number-splitting attack for Bennett-Brassard 1984 quantum key distribution protocol in the presence of high loss: A legitimate user intentionally and randomly replaces signal pulses by multi-photon pulses (decoy-states). Then they check the loss of the decoy-states. If the loss of the decoy-states is abnormally less than that of signal pulses, the whole protocol is aborted. Otherwise, to continue the protocol, they estimate loss of signal multi-photon pulses based on that of decoy-states. This estimation can be done with an assumption that…
The existing decoy-state quantum key distribution (QKD) beating photon-number-splitting (PNS) attack provides a more accurate method to estimate 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 confirm that there is no attack. In this paper, under the null hypothesis of no 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 p…
Every security analysis of quantum key distribution (QKD) relies on a faithful modeling of the employed quantum states. Many photon sources, like for instance a parametric down conversion (PDC) source, require a multi-mode description, but are usually only considered in a single-mode representation. In general, the important claim in decoy-based QKD protocols for indistinguishability between signal and decoy states does not hold for all sources. We derive new bounds on the single photon transmission probability and error rate for multi-mode states, and apply these bounds to the output state of…
Decoy state and purification protocols for superior quantum key distribution with imperfect quantum-dot based single photon sources: Theory and Experiment
We propose a quantum key distribution scheme which closely matches the performance of a perfect single photon source. It nearly attains the physical upper bound in terms of key generation rate and maximally achievable distance. Our scheme relies on a practical setup based on a parametric downconversion source and present-day, non-ideal photon-number detection. Arbitrary experimental imperfections which lead to bit errors are included. We select decoy states by classical post-processing. This allows to improve the effective signal statistics and achievable distance.
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.
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…
Quantum cryptography or, more precisely, quantum key distribution (QKD), is one of the advanced areas in the field of quantum technologies. The confidentiality of keys distributed with the use of QKD protocols is guaranteed by the fundamental laws of quantum mechanics. This paper is devoted to the decoy state method, a countermeasure against vulnerabilities caused by the use of coherent states of light for QKD protocols whose security is proved under the assumption of single-photon states. We give a formal security proof of the decoy state method against all possible attacks. We compare two wi…
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.
Photon number resolving detectors can enhance the performance of many practical quantum cryptographic setups. In this paper, we employ a simple method to estimate the statistics provided by such a photon number resolving detector using only a threshold detector together with a variable attenuator. This idea is similar in spirit to that of the decoy state technique, and is specially suited for those scenarios where only a few parameters of the photon number statistics of the incoming signals have to be estimated. As an illustration of the potential applicability of the method in quantum communi…
The theoretical existence of photon-number-splitting attacks creates a security loophole for most quantum key distribution (QKD) demonstrations that use a highly attenuated laser source. Using ultra-low-noise, high-efficiency transition-edge sensor photodetectors, we have implemented the first version of a decoy-state protocol that incorporates finite statistics without the use of Gaussian approximations in a one-way QKD system, enabling the creation of secure keys immune to photon-number-splitting attacks and highly resistant to Trojan horse attacks over 107 km of optical fiber.
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 $μ'$.
In this paper, for the decoy state method using a finite number of decoy light intensities, we present an improved upper and lower bounds for the asymptotic yield y_n for n-photon states. In particular if all the light intensities are less than or equal to one, they are not only a lower or upper bound, but in fact are the exact minimum or maximum.
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.
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…
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…
The decoy state protocol has been considered to be one of the most important methods to protect the security of quantum key distribution (QKD) with a weak coherent source. Here we test two experimental approaches to generating the decoy states with different intensities: modulation of the pump current of a semiconductor laser diode, and external modulation by an optical intensity modulator. The former approach shows a side-channel in the time domain that allows an attacker to distinguish s signal state from a decoy state, breaking a basic assumption in the protocol. We model a photon-number-sp…
In practical decoy-state quantum key distribution, the raw key length is finite. Thus, deviation of the estimated single photon yield and single photon error rate from their respective true values due to finite sample size can seriously lower the provably secure key rate $R$. Current method to obtain a lower bound of $R$ follows an indirect path by first bounding the yields and error rates both conditioned on the type of decoy used. These bounds are then used to deduce the single photon yield and error rate, which in turn are used to calculate a lower bound of the key rate $R$. Here I show how…
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.
The privacy amplification term, of which the lower bound needs to be estimated with the decoy-state method, plays a positive role in the secure key rate formula for decoy-state quantum key distribution. In previous work, the yield and the bit error rate of single-photon state are estimated separately to gain this lower bound. In this work, we for the first time take the privacy amplification term as a whole to consider this lower bound. The mathematical description for the correlation between the yield and the bit error rate of single-photon state is given with just two unknown variables. Base…
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.
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.
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 (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 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.
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…
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.
Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. While active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty {\it et al.}, Opt. Lett. {\bf 34}, 3238 (2009).] Thi…
In order to improve the key rate of the decoy-state method, we need to jointly study yields of different bases. Given the delicate fact that pulses of the same preparation state can have different counting rates if they are measured in different bases, for example, those vacuum pulses and those single-photon pulses, existing results of decoy-state quantum key distribution using biased bases are actually flawed by assuming that they are equal. We fix this flaw through using the idea that yields of pulses prepared in different bases are same provided that they are prepared in the same state and …
In order to beat any type of photon-number-splitting attack, we propose a protocol for quantum key distributoin (QKD) using 4 different intensities of pulses. They are vacuum and coherent states with mean photon number $μ,μ'$ and $μ_s$. $μ_s$ is around 0.55 and this class of pulses are used as the main signal states. The other two classes of coherent states ($μ,μ'$) are also used signal states but their counting rates should be studied jointly with the vacuum. We have shown that, given the typical set-up in practice, the key rate from the main signal pulses is quite close to the theoretically …
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…
