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 allowed maximal rate in the case given the small overall transmittance of $10^{-4}$.
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.
The existing theory of decoy-state quantum cryptography assumes the exact control of each states from Alice's source. Such exact control is impossible in practice. We develop the theory of decoy-state method so that it is unconditionally secure even there are state errors of sources, if the range of a few parameters in the states are known. This theory simplifies the practical implementation of the decoy-state quantum key distribution because the unconditional security can be achieved with a slightly shortened final key, even though the small errors of pulses are not corrected.
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.
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, 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,…
We present a secure network communication system that operated with decoy-state quantum cryptography in a real-world application scenario. The full key exchange and application protocols were performed in real time among three nodes, in which two adjacent nodes were connected by approximate 20 km of commercial telecom optical fiber. The generated quantum keys were immediately employed and demonstrated for communication applications, including unbreakable real-time voice telephone between any two of the three communication nodes, or a broadcast from one node to the other two nodes by using one-…
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.
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.
We show that the three-intensity protocol for measurement device independent quantum key distribution (MDI QKD) can be done with different light intensities in {\em only one} basis. Given the fact that the exact values yields of single-photon pairs in the $X$ and $Z$ bases must be the same, if we have lower bound of the value in one basis, we can also use this as the lower bound in another basis. Since in the existing set-up for MDI-QKD, the yield of sources in different bases are normally different, therefore our method can improve the key rate drastically if we choose to only use the lower b…
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.
We present a review on the historic development of the decoy state method, including the background, principles, methods, results and development. We also clarify some delicate concepts. Given an imperfect source and a very lossy channel, the photon-number-splitting (PNS) attack can make the quantum key distribution (QKD) in practice totally insecure. Given the result of ILM-GLLP, one knows how to distill the secure final key if he knows the fraction of tagged bits. The purpose of decoy state method is to do a tight verification of the the fraction of tagged bits. The main idea of decoy-state …
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. …
A highly attenuated laser pulse which gives a weak coherent state is widely used in quantum key distribution (QKD) experiments. A weak coherent state has multi-photon components, which opens up a security loophole to the sophisticated eavesdropper. With a small adjustment of the hardware, we prove that the decoy state method can close this loophole and substantially improve the QKD performance. We also propose a few practical decoy state protocols, study statistical fluctuations and perform experimental demonstrations. Moreover, we apply the methods from entanglement distillation protocols bas…
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 measurement-device-independent quantum key distribution (MDI-QKD) possesses the highest security among all practical quantum key distribution protocols. However, existing multi-intensity decoy-state methods may cause loopholes when modulating light intensities with practical devices. In this paper, we propose a passive decoy-state MDI-QKD protocol based on a novel structure of heralded single-photon sources. It does not need to modulate the light source into different intensities and thus can avoid leaking modulation information of decoy states to eavesdroppers, enhancing the security of p…
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 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.
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.
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.
In practical quantum key distribution, weak coherent state is often used and the channel transmittance can be very small therefore the protocol could be totally insecure under the photon-number-splitting attack. We propose an efficient method to verify the upper bound of the fraction of counts caused by multi-photon pluses transmitted from Alice to Bob, given whatever type of Eve's action. The protocol simply uses two coherent states for the signal pulses and vacuum for decoy pulse. Our verified upper bound is sufficiently tight for QKD with very lossy channel, in both asymptotic case and non-…
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…
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…
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 …
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…
The performance of a QKD implementation is determined by the tightness of the underlying security analysis. In particular, the security analyses determines the key-rate, i.e., the amount of cryptographic key material that can be distributed per time unit. Nowadays, the security analyses of various QKD protocols are well understood. It is known that optimal protocol parameters, such as the number of decoy states and their intensities, can be found by solving a nonlinear optimization problem. The complexity of this optimization problem is typically handled by making an number of heuristic assump…
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…
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…
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…
The BB84 quantum key distribution (QKD) combined with decoy-state method is currently the most practical protocol, which has been proved secure against general attacks in the finite-key regime. Thereinto, statistical fluctuation analysis methods are very important in dealing with finite-key effects, which directly affect secret key rate, secure transmission distance and even the most important security. There are two tasks of statistical fluctuation in decoy-state BB84 QKD. One is the deviation between expected value and observed value for a given expected value or observed value. The other is…
We present results of practical sending-or-not quantum key distribution. In real-life implementations, we need consider the following three requirements, a few different intensities rather than infinite number of different intensities, a phase slice of appropriate size rather than infinitely small size and the statistical fluctuations. We first show the decoy-state method with only a few different intensities and a phase slice of appropriate size. We then give a statistical fluctuation analysis for the decoy-state method. Numerical simulation shows that, the performance of our method is compar…
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 demonstrate the decoy-state quantum key distribution (QKD) with one-way quantum communication in polarization space over 102km. Further, we simplify the experimental setup and use only one detector to implement the one-way decoy-state QKD over 75km, with the advantage to overcome the security loopholes due to the efficiency mismatch of detectors. Our experimental implementation can really offer the unconditionally secure final keys. We use 3 different intensities of 0, 0.2 and 0.6 for the pulses of source in our experiment. In order to eliminate the influences of polarization mode dispersio…
Alice communicates with words drawn uniformly amongst $\{\ket{j}\}_{j=1..n}$, the canonical orthonormal basis. Sometimes however Alice interleaves quantum decoys $\{\frac{\ket{j}+i\ket{k}}{\sqrt{2}}\}$ between her messages. Such pairwise superpositions of possible words cannot be distinguished from the message words. Thus as malevolent Eve observes the quantum channel, she runs the risk of damaging the superpositions (by causing a collapse). At the receiving end honest Bob, whom we assume is warned of the quantum decoys' distribution, checks upon their integrity with a measurement. The present…
In this paper, we consider the decoy-state Measurement-Device-Independent Quantum key distribution (MDI-QKD) with four intensities. The average value of successful events and bit errors among the pulse pair set be used to investigate the successful events of different pulses under the statistical fluctuation caused by the finite condition. We demonstrate that the lower bound of successful events number n11estimated by our method can be more tight than the result in [28]. Numerical simulations show that our estimation method can achieve a higher key rate than existing methods with a relatively …
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…
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…
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 this article we present a new prepare and measure quantum key distribution protocol that decouples the necessary quantum channel error estimation from its dependency on sifting, or otherwise post-selecting, the detection outcomes. Rather than estimating Eve's coupling to the quantum channel from the statistics of the sifted key, we infer this information from weak measurements made equally on all of the received photons immediately prior to post-selection by the photon detectors. We prove that the accuracy of the weak measurement parameter estimation is robust to reasonable device imperfect…
The measurement-device-independent quantum key distribution (MDI-QKD) protocol is proposed to remove the detector side channel attacks, while its security relies on the assumption that the encoding systems are perfectly characterized. In contrast, the MDI-QKD protocol based on the Clauser-Horne-Shimony-Holt inequality (CHSH-MDI-QKD) weakens this assumption, which only requires the quantum state to be prepared in the two-dimensional Hilbert space and the devices are independent. In experimental realizations, the weak coherent state, which is always used in QKD systems due to the lack of an idea…
Position-based quantum cryptography (PBQC) allows a party to use its geographical location as its only credential to implement various cryptographic protocols. Such a protocol may lead to important applications in practice. Although it has been shown that any PBQC protocol is breakable if the adversaries pre-share an arbitrarily large entangled state, the security of PBQC in the bounded-quantum-storage model is still an open question. In this paper, we study the performance of various PBQC protocols over a lossy channel under the assumption that no entanglement is pre-shared between adversarie…
An efficient quantum cryptography network protocol is proposed with d-dimension polarized photons, without resorting to entanglement and quantum memory. A server on the network, say Alice, provides the service for preparing and measuring single photons whose initial state are |0>. The users code the information on the single photons with some unitary operations. For preventing the untrustworthy server Alice from eavesdropping the quantum lines, a nonorthogonal-coding technique (decoy-photon technique) is used in the process that the quantum signal is transmitted between the users. This protoco…
A novel protocol - measurement-device-independent quantum key distribution (MDI-QKD) - removes all attacks from the detection system, the most vulnerable part in QKD implementations. In this paper, we present an analysis for practical aspects of MDI-QKD. To evaluate its performance, we study various error sources by developing a general system model. We find that MDI-QKD is highly practical and thus can be easily implemented with standard optical devices. Moreover, we present a simple analytical method with only two (general) decoy states for the finite decoy-state analysis. This method can be…
The binary (one-bit-per-photon) encoding that most existing quantum key distribution (QKD) protocols employ puts a fundamental limit on their achievable key rates, especially under high channel loss conditions associated with long-distance fiber-optic or satellite-to-ground links. Inspired by the pulse-position-modulation (PPM) approach to photon-starved classical communications, we design and demonstrate the first PPM-QKD, whose security against collective attacks is established through continuous-variable entanglement measurements that also enable a novel decoy-state protocol performed conve…
Twin-Field (TF) quantum key distribution (QKD) is a major candidate to be the new benchmark for far-distance QKD implementations, since its secret key rate can overcome the repeaterless bound by means of a simple interferometric measurement. Many variants of the original protocol have been recently proven to be secure. Here, we focus on the TF-QKD type protocol proposed by Curty et al [preprint arXiv:1807.07667], which can provide a high secret key rate and whose practical feasibility has been demonstrated in various recent experiments. The security of this protocol relies on the estimation of…
We present formulas to tightly upper bound the phase-flip errors in decoy state method by using 4 intensities. Our result compressed the bound to about a quarter of known result for MDI-QKD. Based on this, we find that the key rate is improved by more than $100\%$ given weak coherent state sources (WCS), and even more than $200\%$ with the heralded single-photon sources (HSPS).
We present the method of decoy-state analysis after bit-flip error correction and using confidential observed numbers. Taking this tool we then construct a universal approach to sending-or-not-sending (SNS) protocol of twin-field quantum key distribution. In this improved protocol, the code bits are not limited to heralded events in time windows participated by pulses of intensity $μ_z$ and vacuum. All kinds of heralded events can be used for code bits to distill the final keys. The number of intensities (3 or 4) and the kinds of heralded events for code bits are automatically chosen by the ke…
Quantum key distribution (QKD) based on the laws of quantum physics allows the secure distribution of secret keys over an insecure channel. Unfortunately, imperfect implementations of QKD compromise its information-theoretical security. Measurement-device-independent quantum key distribution (MDI-QKD) is a promising approach to remove all side channels from the measurement unit, which is regarded as the "Achilles' heel" of QKD. An essential assumption in MDI-QKD is however that the sources are trusted. Here we experimentally demonstrate that a practical source based on a semiconductor laser di…
As an essential application of quantum mechanics in classical cryptography, quantum secret sharing has become an indispensable component of quantum internet. Recently, a differential phase shift quantum secret sharing protocol using a twin field has been proposed to break the linear rate-distance boundary. However, this original protocol has a poor performance over channels with asymmetric transmittances. To make it more practical, we present a differential phase shift quantum secret sharing protocol with asymmetric source intensities and give the security proof of our protocol against individ…
Twin-Field quantum key distribution (TF-QKD) can beat the linear bound of repeaterless QKD systems. After the proposal of the original protocol, multiple papers have extended the protocol to prove its security. However, these works are limited to the case where the two channels have equal amount of loss (i.e. are symmetric). In a practical network setting, it is very likely that the channels are asymmetric due to e.g. geographical locations. In this paper we extend the "simple TF-QKD" protocol to the scenario with asymmetric channels. We show that by simply adjusting the two signal states of t…
