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 work establishes, in the case of individual attacks, the tradeoff between Eve's information gain (her chances, if a message word was sent, of guessing which) and the disturbance she induces (Bob's chances, if a quantum decoy was sent, to detect tampering). Besides secure channel protocols, quantum decoys seem a powerful primitive for constructing n-dimensional quantum cryptographic applications. Moreover the methods employed in this article should be of strong interest to anyone concerned with the old but fundamental problem of how much information may be gained about a system, versus how much this will disturb the system, in quantum mechanics. Keywords: d-level systems cryptography
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 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.
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.
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 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 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.
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.
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 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 $μ'$.
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.
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 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 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.
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…
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.
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 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 …
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.
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 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.
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.
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…
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…
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 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.
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.
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.
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 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.
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 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.
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 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 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 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 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}.
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…
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 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.
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 …
We propose a quantum key distribution scheme that combines a biased basis choice with the decoy-state method. In this scheme, Alice sends all signal states in the $Z$ basis and decoy states in the $X$ and $Z$ basis with certain probabilities, and Bob measures received pulses with optimal basis choice. This scheme simplifies the system and reduces the random number consumption. From the simulation result taking into account of statistical fluctuations, we find that in a typical experimental setup, the proposed scheme can increase the key rate by at least 45% comparing to the standard decoy-stat…
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…
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…
As a promising quantum key distribution (QKD), most of the existing round-robin differential-phase-shift quantum key distribution (RRDPS-QKD) protocols have adopted the decoy-state method and have assumed the source states are exactly controlled. However, the precise manipulation of source states is impossible for any practical experiment, and the RRDPS-QKD with source errors has an unignorable impact on the performance of the protocol. In the paper, we study the three-intensity decoy-state RRDPS-QKD protocol with source errors, formulate the secure generation key rate of the proposed protocol…
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…
To the active basis choice decoy state quantum key distribution systems with detector efficiency mismatch, we present a modified attack strategy, which is based on faked states attack, with quantum nondemolition measurement ability to restress the threat of detector efficiency mismatch. Considering that perfect quantum nondemolition measurement ability dose not exist in real life, we also propose a practical attack strategy using photon number resolving detectors. Theoretical analysis and numerical simulation results show that, without changing the channel, our attack strategies are serious th…
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…
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 …
Let $\ket{\0}$ and $\ket{\1}$ be two states that are promised to come from known subsets of orthogonal subspaces, but are otherwise unknown. Our paper probes the question of what can be achieved with respect to the basis $\{\ket{\0},\ket{\1}}^{\otimes n}$ of $n$ logical qubits, given only a few copies of the unknown states $\ket{\0}$ and $\ket{\1}$. A phase-invariant operator is one that is unchanged under the relative phase-shift $\ket{\1} \mapsto e^{i θ}\ket{\1}$, for any $θ$, of all of the $n$ qubits. We show that phase-invariant unitary operators can be implemented exactly with no copies a…
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…
To overcome the signal disturbance from the transmission process, recently, a new type of protocol named round-robin differential-phase-shift(RRDPS) quantum key distribution[Nature 509, 475(2014)] is proposed. It can estimate how much information has leaked to eavesdropper without monitoring bit error rates. In this paper, we compare the performance of RRDPS using different sources without and with decoy-state method, such as weak coherent pulses(WCPs) and heralded single photon source(HSPS). For practical implementations, we propose finite decoy-state method for RRDPS, the performance of whic…
There is considerable interest in predicting the efficiency of Quantum Key Distribution (QKD) protocols when one of their implementation quantities is modified. One significant imperfection that affects the efficiency of the setup is the afterpulse phenomenon which consists in the spontaneous detections triggered by trapped carriers after previous avalanches at the detectors. While it is widely studied in bibliography for various QKD protocols, it has been reported much more scarcely for the well-known decoy-state QKD protocols and for dual detectors only. We develop a theoretical analysis of …
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.
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.
