Abstract
Quantum key distribution (QKD) promises unconditional security in data communication and is currently being deployed in commercial applications. Nonetheless, before QKD can be widely adopted, it faces a number of important challenges such as secret key rate, distance, size, cost and practical security. Here, we survey those key challenges and the approaches that are currently being taken to address them.
Introduction
Why quantum key distribution?
For thousands of years, human beings have been using codes to keep secrets. With the rise of the Internet and recent trends to the Internet of Things, our sensitive personal financial and health data as well as commercial and national secrets are routinely being transmitted through the Internet. In this context, communication security is of utmost importance. In conventional symmetric cryptographic algorithms, communication security relies solely on the secrecy of an encryption key. If two users, Alice and Bob, share a long random string of secret bits—the key—then they can achieve unconditional security by encrypting their message using the standard onetimepad encryption scheme. The central question then is: how do Alice and Bob share a secure key in the first place? This is called the key distribution problem. Unfortunately, all classical methods to distribute a secure key are fundamentally insecure because in classical physics there is nothing preventing an eavesdropper, Eve, from copying the key during its transit from Alice to Bob. On the other hand, standard asymmetric or publickey cryptography solves the key distribution problem by relying on computational assumptions such as the hardness of factoring. Therefore, such schemes do not provide informationtheoretic security because they are vulnerable to future advances in hardware and algorithms, including the construction of a largescale quantum computer.^{1}
We remark that some secrets, for instance, census data, need to be kept secret for decades (e.g. 92 years in Canada (Statistical Canada webpage. Release of personal data after 92 years, URL: http://www12.statcan.gc.ca/censusrecensement/2011/ref/aboutapropos/personalpersonnelseng.cfm)). Currently, however, data transmitted in 2016 is vulnerable to technological advances made in the future as Eve might simply save the transcripts of communication in her memory and wait for the construction, for example, of a quantum computer some time before 2,108 (92 years from 2016). This is highly probable. Recall that ENIAC, the first general purpose electronics computer,^{2} which was largely inferior to modern computers, was invented only 70 years ago. The US National Security Agency is taking the threat of quantum computing seriously and has recently announced transition plans to quantumresistant classical algorithms^{3} (These algorithms are typically based on hard computational problems involving for instance the structure of some specific lattices. Despite important progress in the development of such algorithms, it is still an open question whether they are secure against a quantum computer).
Quantum cryptography, or more specifically, quantum key distribution (QKD),^{4–7} promises in principle unconditional security—the Holy Grail of communication security—based on the laws of physics only.^{8–10} QKD has the advantage of being futureproof:^{11} unlike classical key distribution, it is not possible for an eavesdropper to keep a transcript of quantum signals sent in a QKD process, owing to the quantum noncloning theorem.^{12,13} For this reason, QKD is an essential element of the future quantumsafe infrastructure, which will include both quantumresistant classical algorithms and quantum cryptographic solutions. In the bigger context of quantum information, there has been tremendous scientific and engineering effort towards the longterm vision of a global quantum internet.^{14} Imagine a world where only a few largescale quantum computers are available (just like the early days of classical computing when only a few classical computers were available and in line with the current trend towards cloud computing); users will have to access those powerful quantum computers at long distances via a quantum internet. QKD will have a central role in securing data communication links in such a quantum internet.
The potential applications of QKD include securing critical infrastructures (for instance, the Smart Grid), financial institutions and national defense. Experimental QKD has been performed over distances on the order of 100 km in standard telecom fibres as well as in free space, while the secure key rate has now reached a few Mbits per second. QKD has leaped out of the lab.^{15} In China, the deployment of a 2,000 km QKD network between Shanghai and Beijing is underway; in Europe, after the SECOQC network demonstration in 2008,^{16} the UK is now creating a quantum network facilitating device and system trials, and the integration of quantum and conventional communications; in Japan, QKD technologies will be put into test to secure transmission of sensitive genome data; and the US has also started installing its own QKD network.
Why practical challenges in QKD?
In this review, we will focus on practical issues in QKD. We remark that, historically, practical considerations in QKD have led to groundbreaking inventions. For example, the need to counter the photonnumbersplitting attack^{17} triggered the invention of the decoystate protocol,^{18–20} which allows efficient distillation of secure keys using weak coherent pulse based QKD systems that once were vulnerable. As another example, the need to counter detector sidechannel attacks has led to the discovery of measurement device independent (MDI) QKD.^{21} New theory that is due to practical advances in QKD also includes, for instance, the quantum de Finetti theorem,^{22} while security loopholes in QKD are closely related to loopholes in Bell inequality tests^{23}—a key subject in the foundations of quantum mechanics. These issues are therefore of great interest to mathematicians and theoretical physicists.
QKD is clearly of interest to engineers too. For instance, practical QKD is closely linked to the development of new singlephoton detection technologies such as superconducting nanowire singlephoton detectors (SNSPDs),^{24} superconducting transitionedge sensors (TES),^{25} frequency upconversion single photon detectors,^{26,27} and selfdifferencing InGaAs avalanche photodiodes,^{28} as well as of highperformance homodyne detection techniques.^{29} It is also the motivation for highspeed quantum random number generators^{30} and broadband entangled photon sources.^{31}
Practical QKD has steered innovation and is a precursor in the field of Quantum Information Processing.
Outline of the review
Despite the important theoretical and experimental achievements, a number of key challenges remain for QKD to be widely used for securing everyday interactions. For instance, much effort is being put into increasing the communication rate and range of QKD and making QKD systems low cost, compact and robust. New hardware such as chipbased QKD and new software such as novel protocols are being studied and developed. The security of practical QKD systems is another important challenge. In order to foil quantum hackers, protocols such as MDIQKD and losstolerant QKD^{32} have been developed and are currently being experimentally implemented. Yet, a comprehensive theory of the model of a QKD source remains to be constructed. To further extend the reach of QKD, two different approaches—quantum repeaters and groundtosatellite QKD—are being pursued. In view of the proliferation of mobile computing devices including smart phones, mobile QKD applications have also attracted recent attention. Furthermore, the standardisation of QKD components is currently being pursued in European Telecommunications Standards Institute.^{33} In what follows, we will highlight some of the above challenges and the various approaches that are being taken to tackle them.
Main protocols and implementations
We begin our discussion with a brief overview of the main QKD protocols currently studied and the stateoftheart in their practical implementations. As our main focus here is the current challenges in the field, we refer the reader to a recent review^{7} for the necessary background on the rigorous informationtheoretic (or, unconditional) security definition of QKD in the composable framework, secure communication schemes including the onetime pad, the standard BB84 QKD protocol, and basic QKD components.
QKD protocols can be in essence divided with respect to the detection technique required to recover the key information encoded in the properties of light (Figure 1a). In discretevariable (DV) protocols information is typically encoded in the polarisation or phase of weak coherent pulses simulating true singlephoton states; hence the corresponding implementations employ singlephoton detection techniques. The previously mentioned BB84 and decoystate protocols are prominent examples in this category. Singlephoton detection techniques are also necessary for the socalled distributedphasereference protocols, such as the coherentoneway^{34} and differentialphaseshift (DPS)^{35} protocols, where the key information is encoded in photon arrival times or in the phase between adjacent weak coherent pulses. On the other hand, in continuousvariable (CV) QKD protocols information is encoded in the quadratures of the quantised electromagnetic field, such as those of coherent states,^{36,37} and homodyne or heterodyne detection techniques are used in this case. Such detectors are routinely deployed in classical optical communications, hence the CV approach offers the possibility for implementations based only on mature telecom components. All these protocols are prepareandmeasure in the sense that the transmitter, Alice, sends the encoded pulses to the receiver, Bob, who decodes as required by the specific protocol. On the contrary, in entanglementbased protocols,^{5} both parties receive parts of an entangled state and perform suitable measurements. More details on all protocols can be found in refs 6,7,38,39.
When it comes to practical demonstrations, performance of pointtopoint links is assessed by the distance over which secret keys can be distributed and the rate of their distribution for a given security level. The security level is determined by the type of attacks considered in the corresponding security proof; demonstrating security against the socalled collective attacks^{6} is an important challenge for an implementation; however, informationtheoretic security is achieved only when security against the most general (or coherent) attacks is proven. Hence, the ultimate goal is to provide this level of security at a speed and a distance that are compatible with practical applications. Some recent implementations have provided high levels of security: several QKD protocols have been demonstrated to provide composable security against collective attacks using reasonable data block sizes and practical setups, including decoystate BB84,^{40} coherentoneway,^{41} and CVQKD.^{42,43} Among those protocols, the security of decoystate BB84 QKD has been extended to cover coherent attacks, for realistic block sizes and with a minimal sacrifice in the secret key rate.^{44,45} Unfortunately, for coherentoneway, the best security proof against coherent attacks currently gives a secret key rate that only scales quadratically with the loss.^{46} For CVQKD with coherent states and heterodyne detection, a composable security proof against the most general attacks has recently been provided,^{47} but the current proof techniques do not allow a positive key rate for realistic block sizes in this case. Extending the security proofs for the latter protocols is therefore a pressing task in the theoretical study of QKD.
Figure 1b,c shows examples of advanced fibreoptic QKD systems allowing for realtime secret key generation over distances of 50 km with Mbit/s rates. In Figure 1d we summarise some important experimental achievements from both established and emerging QKD protocols (discussed in the following sections). Although the security assumptions and technological maturity vary in these implementations, these results illustrate the diversity of protocols and experimental solutions that the research community has invented to push the performance of QKD technology. Indeed, tremendous progress has been achieved in recent years, and avenues for further progress will be discussed in the next section. We remark, however, that there are fundamental limitations on what can be ultimately achieved. Over optical fibre networks, the attenuation of light in standard fibres at the telecom wavelength of 1,550 nm is 0.2 dB/km (or 0.16 dB/km in newly developed ultralow loss fibres). This unavoidable loss will not allow the range of pointtopoint QKD links to exceed a few hundreds of kilometres as with overly excessive channel loss it would take several years to generate just one bit even using perfect light sources and detectors. Furthermore, with a practical lossy channel, the ultimate key rate is upper bounded by the socalled TGW bound^{48} (see also ref. 49 for a more recent result, quoted as the PLOB bound). These bounds provide a useful benchmark for the performance of all QKD protocol implementations.
Major challenges in performance and cost
In the quest for high performance and lowcost QKD systems, both hardware and software solutions are currently being pursued.
Hardware development
Key rate
Encryption keys generated by QKD can be used in a symmetric cipher scheme, such as Advanced Encryption Standard, which is quantum resistant, for enhanced security, or they can be combined with the onetimepad encryption scheme for unconditional security. In both cases, the secure key rate achieved by the underlying QKD layer in a typical application scenario is crucial. Higher secure rates allow for a more frequent update of encryption keys in symmetric ciphers, and for a proportional increase in the onetimepad communication bandwidth as this scheme requires the key to be as long as the message.
Presently, strong disparity exists between the classical and QKD communication rates. Classical optical communications delivering speeds of 100 Gbit/s per wavelength channel are currently being deployed,^{50} and a field trial featuring 54.2 Tbit/s aggregated data rate has recently been performed.^{51} On the other hand, the Mbit/s rates achieved by QKD systems today are sufficient, for instance, for video transmission; however, it is clear that if we want in the longer term to encrypt high volumes of classical network traffic using the onetimepad, major developments on the secure key rate generated by QKD will be required.
The obtained key rate depends crucially on the performance of the detectors used. For QKD systems employing singlephoton detection techniques, high efficiency and short dead time of the detectors are essential for reaching a high bit rate. The latest developments on high efficiency detectors^{52–54} are extremely promising; quantum efficiencies as high as 93% at telecom wavelengths have been reported for SNSPDs,^{53} and devices based on this technology with short dead time, low dark count, low time jitter and high detection efficiency are commercially available^{55} (Figure 2a,b). These results may allow for as much as a fourfold increase in the secret key rate, which currently stands at 1 Mbit/s over a 50 km fibre (or 10 dB loss) achieved using selfdifferencing InGaAs avalanche photodiodes with an ultrashort dead time^{40} (Figure 2c). Further key rate increase is possible using wavelength or spatial mode multiplexing technologies that have been routinely used for increasing the bandwidth in data communications.^{50,56,57} For CVQKD systems, increasing the bandwidth of the homodyne or heterodyne detectors, while keeping at the same time the electronic noise low, is a necessary step for increasing the key rate beyond the 1 Mbit/s over 25 km that has been achieved.^{43} Further progress continues to be pursued, targeting also higher efficiency, which is currently around 60% for fibrecoupled detectors at telecom wavelengths.^{42} Furthermore, as shown in Figure 1c, a practical issue in these systems is that the strong phase reference pulse (or local oscillator) needs to be transmitted together with the signal at high clock rates; recent proposals that avoid this and use instead a local oscillator generated at Bob’s site^{58–60} are promising and will lead to more practical, high performance implementations.
Distance
Extending the communication range of QKD systems is a major driving factor for technological developments in view of future network applications. QKD systems based on singlephoton detection champion the pointtopoint communication distance (or channel loss). Here the low noise of singlephoton detectors is the key enabling factor; in particular, the attainable range depends on the type and operation temperature of the detectors. InGaAs avalanche photodiodes can tolerate losses of 30 and 52 dB when cooled to −30 and −120 °C,^{41,61} respectively, whereas SNSPDs cooled to cryogenic temperatures have been demonstrated to withstand a record loss of 72 dB.^{62} This loss is equivalent to 360 km of standard single mode fibre or about 450 km of ultralow loss fibre. Although technologically possible, further extending the pointtopoint distance is increasingly unappealing because the channel loss will inevitably reduce the key rate to a level of little practical relevance. This is also true for CVQKD systems, which are in general more sensitive to losses. Here it is crucial to keep the excess noise—the noise exceeding the fundamental shot noise of coherent states—low and especially to be able to estimate the noise value precisely, which becomes increasingly difficult with the distance.^{38,42}
We remark that advances towards highperformance QKD systems in terms of key rate and distance are coupled with the security guarantees offered by these systems. For instance, achieving composable security against general attacks requires in practice being able to perform efficient postprocessing, including parameter estimation, over large data blocks with stable setups. Particularly for CVQKD, performing efficient error correction and precise parameter estimation is of utmost importance.^{38,63}
Cost and robustness
For QKD systems to be used in real world applications, low cost and robustness are indispensable features alongside high performance. Several avenues are currently being pursued. First, QKD systems have been shown to coexist with intense data traffic in the same fibre,^{64–67} thus eliminating the need for dark fibres that are not only expensive but also often unavailable. Access network architecture allows simultaneous access by a multitude of QKD users, and importantly they are compatible with full power Gigabit Passive Optical Network traffic in the same network.^{61,68} Roomtemperature singlephoton detectors have been shown to be suitable for DVQKD over up to 100 km fibre, thus removing cooling requirements for the entire QKD system;^{44,69} for CVQKD cooling is unnecessary. All these developments help reduce deployment cost as well as system complexity, footprint and power consumption.
Another important avenue to address the issue of cost and robustness is photonic integration.^{70} Chipscale integration will bring high level of miniaturisation, leading to compact and lightweight QKD modules that can be massmanufactured at low cost. Two main integration platforms are currently being explored, namely silicon (Si)^{71} and indium phosphide (InP),^{72} whereas alternative techniques include lithium niobate (LiNbO_{3}) integration and glass waveguide technologies. For QKD protocols employing singlephoton detection, the main difficulty comes from the receiver side so initial experiments have focused on transmitter integration. A LiNbO_{3} integrated polarisation controller was used for state preparation in a QKD implementation,^{73} whereas several techniques were combined to construct a handheld QKD sender module in ref. 74. More recently, a QKD transmitter chip that is reconfigurable to accommodate the state preparation for several QKD protocols, including decoystate BB84, coherentoneway and DPS, has been developed on InP^{75} (Figure 3), and Si transmitters have also been demonstrated independently by the U. of Toronto^{76} and also by Bristol group. (C. Erven and M. Thompson, private communication.)
Chipscale QKD receivers are also progressing. Lowloss planarlightwavecircuits based on silicaonsilicon technology have been routinely used to replace fibrebased asymmetric Mach–Zehnder interferometres,^{75,77,78} a key enabling component for phasebased QKD protocols. Research efforts are currently focused on the integration of singlephoton detectors using the aforementioned techniques, which will be essential for developing complete integrated systems. CVQKD systems are particularly well suited for this objective because they only require the use of standard components. Indeed, Si photonic chips integrating many functionalities of a CVQKD setup, including active elements such as amplitude and phase modulators and homodyne/heterodyne detectors based on germanium (Ge) photodiodes, have been developed.^{79}
Development of chipscale QKD is still at its early stages. Further research in this direction will help bring the QKD technology closer to its wide adoption.
New QKD protocols
In parallel to hardware development, much effort has also been devoted to novel QKD protocols aiming to outperform the established ones. Encouragingly, this line of research has led to protocols that may exhibit advantages when certain technical constraints are in place. Below, we discuss two protocols featuring high photon information capacity or noise tolerance.
High dimensionQKD
High dimensionQKD allows retrieval of more than 1 bit from each detected photon, thus offering an advantage in the photon information capacity when the photon rate is restrained.^{80–82} The choice for encoding is to use the arrival times of timeenergy entangled photon pairs,^{83} whose continuous nature permits encoding of extremely large alphabets. A security proof against collective attacks has been developed,^{84} which was followed by a laboratory experiment demonstrating a photon information capacity of up to 6.9 bits per coincidence and a key rate of 2.7 Mbit/s over a 20 km fibre.^{85} Although this development has narrowed the key rate gap between entanglement based and prepareandmeasure QKD systems, its viability in a field environment will face a challenge to maintain the near unity interference visibility which was key to the obtained information capacity. High dimensionQKD without entanglement is also possible by exploiting the spatial degree of freedom, but its potential is restricted by the availability of high speed modulators.^{86,87}
RRDPSQKD
The RoundRobin (RR) DPS protocol, which was proposed in 2014,^{88} removes the need for monitoring the channel disturbance to establish security, in stark contrast with conventional QKD protocols (see Figure 4a for the principle). Instead, Eve’s information can be tightly set, even to an arbitrarily low level, by just choosing experimental parameters. In theory, a positive key rate is possible for any quantum bit error rate (QBER) <50%. This extraordinary QBER tolerance makes it attractive for deployment when large systematic errors cannot be avoided. Shortly after its introduction the protocol has stimulated a number of experimental demonstrations.^{89–92} The RRDPSQKD protocol uses a transmitter identical to that found in a conventional DPS system,^{35} but requires a receiver that is capable of measuring the differential phase between any two pulses within a pulse group sent by Alice. Two different approaches are adopted. In the first, direct approach, a combination of optical switches and delay lines is used to bring the intended pulses into temporal overlap and then let them interfere^{90–92} (see for example Figure 4b). A more ingenious approach is to let a common phase reference interfere with all pulses sent by Alice, and then determine the differential phase between those pulses whose interference with the common reference produces a photon click.^{89} This latter approach avoids many problems associated with the direct one, such as loss and phase instability caused by optical delay lines and switches, but it will require remote optical phase locking for optimal performance. As it currently stands, the best key rate for RRDPSQKD is around 10 kbit/s for a 50 km distance in fibre^{91} and cannot compete with the more mature decoystate BB84 protocol. RRDPSQKD has the advantage of being robust against encoding errors,^{93} but it is vulnerable to attacks on detectors, which will be discussed in the next section.
Major challenges in practical security
Although the security of a QKD protocol can be proven rigorously, its reallife implementation often contains imperfections that may be overlooked in the corresponding security proof. By exploiting such imperfections, various attacks, targeting either the source or the detectors, have been proposed; some of them have even been demonstrated to be effective against commercial systems.^{94–96} We refer the reader to a recent review^{7} for more details on quantum hacking and also countermeasures. To regain security in practical QKD, several solutions, including QKD based on testable assumptions,^{7} device independent (DI) QKD^{97,98} (see also ref. 99) and MDIQKD,^{21} have been proposed. In the following, we discuss some important recent developments in this direction.
MDIQKD
One promising longterm solution to sidechannel attacks is DIQKD, where the security relies on the violation of a Bell inequality and can be proven without knowing the implementation details. While recent loopholefree Bell experiments^{23,100,101} imply that DIQKD could be implemented, the expected secure key rate is nevertheless impractically low even at short distances. A more practical solution is MDIQKD, which is inherently immune to all sidechannel attacks targeting the measurement device, usually the most vulnerable part in a QKD system. In fact, the measurement device in MDIQKD can be treated as a ‘black box’ which could even be manufactured and operated by Eve. Building upon refs 102,103; ref. 21 proposed a practical scheme with weak coherent pulses and decoy states (Figure 5a), whose security against the most general coherent attacks, taking into account the finite data size effect, has been proved in ref. 104 (see also ref. 99, which studied an entanglementbased representation with general finitedimensional systems, and ref. 105, which proposed a DIQKD protocol with local Bell test).
MDIQKD^{21} is a natural building block for multiuser QKD networks, since the most expensive and complicated measurement device can be placed in an untrusted relay and shared among many QKD users.^{68} Several groups have demonstrated its feasibility. In particular, DV MDIQKD was demonstrated over 200 km telecom fibre^{106} and 404 km of ultralow loss fibre^{107} in lab conditions, and over 30 km of deployed fibre.^{108} With highly efficient singlephoton detectors, the tolerable channel loss can be as high as 60 dB, which corresponds to 300 km of standard telecom fibre.^{109} A reallife fibre based multiuser MDIQKD network was also implemented recently^{110} (Figure 5c). Moreover, a 1 Mbit/s proofofprinciple MDIQKD experiment was performed,^{111} thus illustrating the high key rate potential of DV MDIQKD. This was also studied in ref. 112 for MDIQKD employing stateoftheart SNSPDs; in Figure 5b, simulation results of the secret key rate in this case show an achievable key rate of 0.01 bit per pulse over 25 km. With a transmission rate of 1 GHz, this corresponds to a secret key rate of 10 Mbit/s, which is sufficient for many cryptographic applications. As a comparison, we also present in Figure 5b the previously mentioned fundamental upper bounds per optical mode.^{48,49} We see that the key rate of DV MDIQKD is only about 2 orders of magnitude away from the TGW bound at a practical distance, hence this protocol is suitable for high speed communications in metropolitan area networks.
It is important to emphasise that one fundamental assumption in MDIQKD is that Eve cannot interfere with Alice and Bob’s state preparation processes. To prevent Eve from having access to quantum signals entering Alice’s or Bob’s labs and interfering with the state preparation process, MDIQKD is commonly implemented using independent laser sources for Alice and Bob. Recently, gigahertzclocked, phaserandomised pulses from independent gainswitched lasers have been demonstrated to interfere with high visibility, by control of the frequency chirp and/or emission jitter.^{111,113}
DDIQKD
One drawback of MDIQKD is that its key rate scales quadratically with the detector efficiency. This is because in most of existing MDIQKD protocols (except for ref. 114), secure keys are distilled from twofold coincidence detection events (In MDIQKD, the secure key rate R scales as T_{A}×η×T_{B}×η, where T_{A} is the channel transmission from Alice to the measurement device, T_{B} is the channel transmission from Bob to the measurement device, and η is the singlephoton detection efficiency (assuming that all detectors have the same efficiency). The overall transmission of the whole channel (from Alice to Bob) is T=T_{A}×T_{B}, hence the key rate R of MDIQKD scales as T×η^{2}. This means that the key rate of MDIQKD scales linearly with the whole channel transmittance (same as the case of conventional QKD and DDIQKD), but quadratically with the detector efficiency.). Recently, the detectordeviceindependent (DDI) QKD protocol, designed to bridge the strong security of MDIQKD with the high efficiency of conventional QKD, was proposed.^{115–117} In this protocol, the legitimate receiver employs a trusted linear optics network to decode information on photons received from an insecure quantum channel, and then performs a Bell state measurement (BSM) using uncharacterised detectors. One important advantage of this approach is that its key rate scales linearly with the detector efficiency. This is achieved by replacing the twophoton BSM scheme in the original MDIQKD protocol (Figure 5a) by a singlephoton BSM scheme.^{118} However, its ability to completely remove detector sidechannel attacks has yet to be proven. Either countermeasures to Trojan horse attacks^{119} or some trustworthiness to the BSM device is still required to establish the security of DDIQKD.^{120} In fact, mathematically the standard BB84 QKD protocol based on a fourstate modulation scheme can be formulated into a DDIQKD protocol.^{121} This highlights the underlying connection between DDIQKD and the BB84 protocol. Finally, we remark that the advantage of DDIQKD compared with MDIQKD becomes insignificant if high detection efficiency detectors are used in both schemes.
CV MDIQKD
The MDIQKD scheme has been extended recently to the CV framework^{122} (see also refs 123,124 for a more restricted security analysis). In the CV framework, both Alice and Bob prepare Gaussianmodulated coherent states and send them to an untrusted third party, Charlie, who measures the correlation between the incoming quantum states. The CV MDIQKD system requires high efficiency (>85%) homodyne detectors for a positive key rate.^{112} This efficiency requirement has been met in recent proofofprinciple laboratory freespace experiments.^{122,125} However, achieving the required efficiencies in a fibrebased optical network setting is more challenging, owing to the detector coupling loss and losses by fibre network interconnects and components^{110} (see also ref. 126 for a different perspective). When high efficiency detectors are in place, CV MDIQKD would require an asymmetric configuration, where Charlie needs to be located close to one of the users. Even in this case, the expected key rate of the stateoftheart CV MDIQKD system drops to zero when the channel loss is above 6 dB (corresponding to 30 km standard telecom fibre).^{112,122} Therefore, for long distance (>30 km) applications, DV MDIQKD is currently the only option available for MDIQKD. A reliable phase reference between Alice and Bob also needs to be established in CV MDIQKD, and may be possible to realise using recently proposed techniques for standard CVQKD.^{58–60} Despite these challenges, CV MDIQKD has the potential for very high key rates, within one order of magnitude from the TGW and PLOB bounds, at relatively short communication distances.
QKD with imperfect sources
Given that the security loopholes associated with the measurement device can be closed by MDIQKD, an important remaining question is how to justify the assumption of trustable quantum state preparation, including singlemode operation, perfect global phase randomisation, no side channels, etc. On one hand, the imperfections in quantum state preparation need to be carefully quantified and taken into account in the security proof; on the other hand, practical countermeasures are required to prevent Trojan horse attacks^{119} on the source.
To address imperfections in quantum state preparation in QKD, a losstolerant protocol was proposed in ref. 32, which makes QKD tolerable to channel loss in the presence of source flaws (see also studies in refs 127,128). On the basis of the assumption that the singlephoton components of the states prepared by Alice remain inside a twodimensional Hilbert space, it was shown that Eve cannot enhance state preparation flaws by exploiting the channel loss and Eve’s information can be bounded by the rejected data analysis.^{129} The intuition for the security of losstolerant QKD protocol can be understood in the following manner. By assuming that the state prepared by Alice is a qubit, it becomes impossible for Eve to perform an unambiguous state discrimination (USD) attack.^{130} Indeed, in order for Eve to perform a USD attack, the states prepared by Alice must be linearly independent; but by having three or more states in a twodimensional space, in general the set of states prepared by Alice is linearly dependent, thus making USD impossible.
The above losstolerant protocol has been further developed and demonstrated experimentally in ref. 131, where the authors implemented decoystate QKD with imperfect state preparation and employed tight finitekey security bounds with composable security against coherent attacks. The work in ref. 32 has also been extended to the finitekey regime in ref. 132, where a wide range of imperfections in the laser source, such as the intensity fluctuations, have been taken into account. In ref. 133, a rigorous security proof of QKD systems using discretephaserandomised coherent states was given, thus removing the requirement for perfect phase randomisation. With respect to this, we note that gainswitched laser diodes are presently the de facto QKD light source, capable of naturally providing phaserandomised coherent pulses at a clock rate of up to 2.5 GHz.^{134,135}
Progress has also been made on enhancing the security of QKD by carefully examining source imperfections in implementations. Refs 136,137 studied the risk of Trojan horse attacks due to back reflections from commonly used optical components in QKD. Similar research was also conducted for CVQKD.^{138} In ref. 139, by using laserinduced damage threshold of singlemode optical fibre to bound the photon numbers in Eve’s Trojan horse pulses, the authors provided quantitative security bounds and a purely passive solution against a general Trojan horse attack.
All the above advances strongly suggest the feasibility of longdistance secure quantum communication with imperfect sources. A promising research direction is to apply the above techniques for QKD with imperfect sources to MDIQKD leading to practical sidechannelfree QKD. To achieve this goal, it is necessary to establish a comprehensive list of assumptions on the sources, and verify them one by one. In a recent experimental demonstration,^{140} the losstolerant protocol is applied to a MDIQKD setting. Such an experiment thus addresses source and detector flaws at the same time.
We end our discussion on practical security by noting that in both classical and quantum cryptography, it is also important to carefully address the risks of sidechannel attacks on the electronics and postprocessing layers. Various sidechannel attacks discovered in classical cryptography, such as the timing attack,^{141} the powermonitoring attack,^{142} and acoustic cryptanalysis,^{143} can also pose threats to quantum cryptography. Closing these side channels requires substantial future efforts.
Network QKD
So far, our discussion has been largely limited to pointtopoint QKD links. Although these links are useful for some applications, QKD network structures must be considered in order to enable access by a greater many users and also to extend the reach and geographical coverage. In addition, the incorporation of mobile QKD nodes for key transports will add to network connection flexibility and allow even greater geographical coverage. In the following, we discuss approaches for building a QKD network and possibilities for future mobile QKD deployment.
Building QKD networks
An important issue in a network setting is the topology that allows for multiple users to access the network. A star topology is suitable for this purpose for relatively short distance (up to 400 km). Imagine a star network where there is at most one intermediate node between any two users, allowing for secure quantum communication among all users without the need for the relay to be trusted. In fact, this approach has already been demonstrated based on the MDIQKD protocol.^{110} The longterm vision is for each user to use a simple and cheap transmitter and outsource all the complicated devices for network control and measurement to an untrusted network operator. As only one set of measurement devices will be needed for such a network that is shared by many users, the cost per user could be kept relatively low. The network provider would then be in a favourable position to deploy stateoftheart technologies including high detection efficiency SNSPDs to enhance the performance of the network and to perform all network management tasks. The important advantage is that the network operator can be completely untrusted without compromising security. Experimental demonstrations of network MDIQKD, either in optical fibres^{110} or in free space, are a major step towards such QKD networks with untrusted relays.
Nonetheless, MDIQKD is limited in distance, hence in order to address the great challenge of extending the distance of secure QKD, three further approaches are possible. The first and the simplest approach is to use trusted relays. This is already feasible with current technology and indeed has been used as the standard in existing QKD networks.^{16,144} By setting up trusted nodes, for instance, every 50 km, to relay secrets, it is possible to achieve secure communication over arbitrarily long distances. The QKD network currently under development between Shanghai and Beijing is based on this approach.
The second approach is quantum repeaters, which remove the need for the users to trust the relay nodes. Quantum repeaters are beyond current technology, but have been a subject of intense research efforts in recent years. The longterm vision here is to construct a global quantum internet as described, for example, in ref. 14. Research efforts on quantum repeaters have focused on matter quantum memories and their interface with photonic flying qubits.^{145,146} However, new recent approaches manage to reduce the need for a quantum memory^{147} or to completely remove it by using allphotonic quantum repeaters.^{148}
Finally, the third approach is groundtosatellite QKD. By using one or a few trusted satellites as relay stations, it is possible to extend the distance of secure QKD to the global scale. To this end, several freespace studies, including experiments with low earth orbit (LEO) satellites, have been conducted.^{149–155} China, the EU and Canada are all currently exploring experimental groundtosatellite QKD in ambitious longterm projects involving LEO satellites.
Mobile QKD
The studies in freespace QKD may also open the door to mobile QKD networks, which can be useful in many applications, such as shiptoship communication, airport traffic control, communication between autonomous vehicles, etc. In such a network, the mobility of QKD platforms requires the network to be highly reconfigurable—the QKD users should be able to automatically determine the optimal QKD route in real time based on their locations. Fastbeam tracking systems are indispensable. Furthermore, due to the strong ambient light, an effective filtering scheme is required to selectively detect quantum signals. Recent studies analyze the effect of fading and of atmospheric turbulence to CVQKD^{156} and show that CVQKD with coherent detection could be robust against ambient noise photons due to the intrinsic filtering function of the local oscillator.^{157} We also note that preliminary studies suggest that QKD at microwave wavelengths, which are widely used in wireless communications, might be feasible over short distances.^{158–160} Driven by various potential applications, we expect that mobile QKD will become an active research topic in the coming years.
Conclusion
In this review, we have discussed important challenges in practical QKD. These range from extending security proofs to the most general attacks allowed by quantum mechanics to developing photonic chips as well as sidechannelfree systems and globalscale QKD networks. Addressing these challenges using some of the approaches that we have presented will open the way to the use of QKD technology for securing everyday interactions.
As the lead application of the field of Quantum Information Processing, advances in QKD will have important implications in many other applications too. For example, a great range of quantum communication protocols beyond QKD have been studied in recent years^{161} and their development has directly benefited from research in QKD. These include, for instance, quantum bit commitment,^{162–164} quantum secret sharing,^{165–167} quantum coin flipping,^{168,169} quantum fingerprinting,^{170,171} quantum digital signatures,^{172,173} blind quantum computing^{174,175} and positionbased quantum cryptography.^{176–178} It is known that some of those protocols, such as quantum bit commitment and positionbased quantum cryptography, cannot be perfectly achieved with unconditional security. However, other security models exist, such as, for instance, those based on relativistic constraints or on noisy storage assumptions,^{179} where by assuming that it is impossible for an eavesdropper to store quantum information for a long time, one can retrieve security for such protocols.
Determining the exact power and limitations of quantum communication is the subject of intense research efforts worldwide. The formidable developments that can be expected in the next few years will mark important milestones towards the quantum internet of the future.
Notes added in proof
After a completion of a preliminary version of this paper, a recent preprint^{181} has been posted on the arXiv that demonstrates the insecurity of DDIQKD protocol. In addition, it has come to our attention that DIQKD remains vulnerable to covert channels such as memory attack.^{182}
References
Shor, P. W. Proceedings of the 35th Annual Symposium on Foundations of Computer Science (ed. Goldwasser, S.) 124–134 (IEEE Computer Society Press, 1994).
Encyclopedia Britannica. ENIAC. https://www.britannica.com/technology/ENIAC.
Cesare, C. Encryption faces quantum foe. Nature 525, 167–168 (2015).
Bennett, C. H. & Brassard, G. Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (ed. Goldwasser, S.) 175–179 (IEEE Press, 1984).
Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991).
Scarani, V. et al. The security of practical quantum key distribution. Rev. Mod. Phys. 81, 1301 (2009).
Lo, H.K., Curty, M. & Tamaki, K. Secure quantum key distribution. Nat. Photon. 8, 595–604 (2014).
Mayers, D. Unconditional security in quantum cryptography. J. ACM 48, 351–406 (2001).
Lo, H.K. & Chau, H. F. Unconditional security of quantum key distribution over arbitrarily long distances. Science 283, 2050–2056 (1999).
Shor, P. W. & Preskill, J. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000).
Unruh, D. Advances in Cryptology—Crypto 2013. Vol. 8043, 380–397 (Springer, 2013).
Wootters, W. K. & Zurek., W. H. A single quantum cannot be cloned. Nature 299, 802–803 (1982).
Dieks, D. Communication by EPR devices. Phys. Lett. 92A, 271–272 (1982).
Kimble., H. J. The quantum internet. Nature 453, 1023–1030 (2008).
Qiu, J. Quantum communications leap out of the lab. Nature 508, 441–442 (2014).
Peev, M. et al. The SECOQC quantum key distribution in vienna. New J. Phys. 11, 075001 (2009).
Huttner, B., Imoto, N., Gisin, N. & Mor, T. Quantum cryptography with coherent states. Phys. Rev. A 51, 1863–1869 (1995).
Hwang, W.Y. Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003).
Lo, H.K., Ma, X. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).
Wang, X.B. Beating photonnumbersplitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).
Lo, H.K., Curty, M. & Qi, B. Measurementdeviceindependent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012).
Christandl, M., Koenig, R., Mitchison, G. & Renner, R. Oneandahalf quantum de Finetti theorems. Commun. Math. Phys 273, 473–498 (2007).
Hensen, B. et al. Experimental loopholefree violation of a Bell inequality using entangled electron spins separated by 1.3 km. Nature 526, 682 (2015).
Gol’Tsman, G. N. et al. Picosecond superconducting singlephoton optical detector. Appl. Phys. Lett. 79, 705–707 (2001).
Lita, A. E., Miller, A. J. & Nam., S. W. Counting nearinfrared singlephotons with 95% efficiency. Opt. Express 16, 3032–3040 (2008).
Albota, M. A. & Wong, F. N. C. Efficient singlephoton counting at 1.55 μm by means of frequency upconversion. Opt. Lett. 29, 1449–1451 (2004).
Langrock, C. et al. Highly efficient singlephoton detection at communication wavelengths by use of upconversion in reverseprotonexchanged periodically poled LiNbO3 waveguides. Opt. Lett. 30, 1725–1727 (2005).
Yuan, Z. L., Kardynal, B. E., Sharpe, A. W. & Shields, A. J. High speed single photon detection in the near infrared. Appl. Phys. Lett. 91, 041114 (2007).
Hansen, H. et al. Ultrasensitive pulsed, balanced homodyne detector: application to timedomain quantum measurements. Opt. Lett. 26, 1714–1716 (2001).
Jennewein, T., Achleitner, U., Weihs, G., Weinfurter, H. & Zeilinger, A. A fast and compact quantum random number generator. Rev. Sci. Instrum. 71, 1675–1680 (2000).
Zhu, E. Y. et al. Poledfiber source of broadband polarizationentangled photon pairs. Opt. Lett. 38, 4397–4400 (2013).
Tamaki, K., Curty, M., Kato, G., Lo, H.K. & Azuma, K. Losstolerant quantum cryptography with imperfect sources. Phys. Rev. A 90, 052314 (2014).
Alléaume, R. et al. Worldwide standardization activity for quantum key distribution. In Proceedings of the IEEE Globecom Workshops (GC Wkshps), 656–551 (2014).
Stucki, D., Brunner, N., Gisin, N., Scarani, V. & Zbinden, H. Fast and simple oneway quantum key distribution. Appl. Phys. Lett. 87, 194108 (2005).
Inoue, K., Waks, E. & Yamamoto, Y. Differential phase shift quantum key distribution. Phys. Rev. Lett. 89, 037902 (2002).
Grosshans, F. & Grangier, P. Continuous variable quantum cryptography using coherent states. Phys. Rev. Lett. 88, 057902 (2002).
Grosshans, F. et al. Quantum key distribution using gaussianmodulated coherent states. Nature 421, 238 (2003).
Diamanti, E. & Leverrier, A. Distributing secret keys with quantum continuous variables: principle, security and implementations. Entropy 17, 6072–6092 (2015).
Ma, X., Fung, C.H. F. & Lo, H.K. Quantum key distribution with entangled photon sources. Phys. Rev. A 76, 012307 (2007).
Lucamarini, M. et al. Efficient decoystate quantum key distribution with quantified security. Opt. Express 21, 24550–24565 (2013).
Korzh, B. et al. Provably secure and practical quantum key distribution over 307 km of optical fibre. Nat. Photon. 9, 163–168 (2015).
Jouguet, P., KunzJacques, S., Leverrier, A., Grangier, P. & Diamanti, E. Experimental demonstration of longdistance continuousvariable quantum key distribution. Nat. Photon. 7, 378 (2013).
Huang, D. et al. Continuousvariable quantum key distribution with 1 Mbit/s secure key rate. Opt. Express 23, 17511–17519 (2015).
Lim, C. C. W., Curty, M., Walenta, N., Xu, F. & Zbinden, H. Concise security bounds for practical decoystate quantum key distribution. Phys. Rev. A 89, 022307 (2014).
Lucamarini, M., Dynes, J. F., Fröhlich, B., Yuan, Z. & Shields, A. J. Security bounds for efficient decoystate quantum key distribution. IEEE J. Sel. Topics Quantum Electron 21, 6601408 (2015).
Moroder, T. et al. Security of distributedphasereference quantum key distribution. Phys. Rev. Lett. 109, 260501 (2012).
Leverrier, A. Composable security proof for continuousvariable quantum key distribution with coherent states. Phys. Rev. Lett. 114, 070501 (2015).
Takeoka, M., Guha, S. & Wilde, M. M. Fundamental rateloss tradeoff for optical quantum key distribution. Nat. Commun. 5, 5235 (2014).
Pirandola, S., Laurenza, R., Ottaviani, C. & Banchi., L. The ultimate rate of quantum cryptography. Preprint at arXiv:1510.08863 (2015).
Winzer, P. J. Scaling optical fiber networks: Challenges and solutions. Opt. Photon. News 26, 28–35 (2015).
Huang, M. F. et al. Terabit/s Nyquist superchannels in high capacity fiber field trials using DP16QAM and DP8QAM modulation formats. J. Lightw. Technol. 32, 776–782 (2014).
Pernice, W. H. P. et al. Highspeed and highefficiency travelling wave singlephoton detectors embedded in nanophotonic circuits. Nat. Commun. 3, 1325 (2012).
Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).
Comandar, L. C. et al. Gigahertzgated InGaAs/InP singlephoton detector with detection efficiency exceeding 55% at 1550 nm. J. Appl. Phys. 117, 083109 (2015).
Scontel Superconducting nanotechnology. http://www.scontel.ru/; Single Quantum. http://www.singlequantum.com/; ID Quantique. http://www.idquantique.com/; Photon Spt. http://www.photonspot.com/ Accessed 19 October, 2016.
Bahrani, S., Razavi, M. & Salehi, J. A. Orthogonal frequencydivision multiplexed quantum key distribution. J. Lightw. Technol. 33, 4687–4698 (2015).
Dynes, J. F. et al. Quantum key distribution over multicore fiber. Opt. Express 24, 8081–8087 (2016).
Qi, B., Lougovski, P., Pooser, R., Grice, W. & Bobrek, M. Generating the local oscillator ‘locally’ in continuousvariable quantum key distribution based on coherent detection. Phys. Rev. X 5, 041009 (2015).
Soh, D. B. S. et al. Selfreferenced continuousvariable quantum key distribution. Phys. Rev. X 5, 041010 (2015).
Huang, D., Huang, P., Lin, D., Wang, C. & Zeng., G. Highspeed continuousvariable quantum key distribution without sending a local oscillator. Opt. Lett. 40, 3695–3698 (2015).
Fröhlich, B. et al. Quantum secured gigabit optical access networks. Sci. Rep. 5, 18121 (2015).
Shibaba, H., Honjo, T. & Shimizu, K. Quantum key distribution over a 72 dB channel loss using ultralow dark count superconducting singlephoton detectors. Opt. Lett. 39, 5078–5081 (2014).
Jouguet, P., Elkouss, D. & KunzJacques, S. High bit rate continuousvariable quantum key distribution. Phys. Rev. A 90, 042329 (2014).
Patel, K. A. et al. Quantum key distribution for 10 Gb/s dense wavelength division multiplexing networks. Appl. Phys. Lett. 104, 051123 (2014).
Choi, I. et al. Field trial of a quantum secured 10 Gb/s DWDM transmission system over a single installed fiber. Opt. Express 22, 23121–23128 (2014).
Qi, B., Zhu, W., Qian, L. & Lo, H.K. Feasibility of quantum key distribution through a dense wavelength division multiplexing network. New J. Phys. 12, 103042 (2010).
Kumar, R., Qin, H. & Alléaume, R. Coexistence of continuous variable QKD with intense DWDM classical channels. New J. Phys. 17, 043027 (2015).
Fröhlich, B. et al. A quantum access network. Nature 501, 69–72 (2013).
Comandar, L. C. et al. Room temperature singlephoton detectors for high bit rate quantum key distribution. Appl. Phys. Lett. 104, 021101 (2014).
Hughes, R. J. et al. Networkcentric quantum communications with applications to critical infrastructure protection. Preprint at arXiv:1305.0305 (2013).
Lim, A. E.J. et al. Review of silicon photonics foundry efforts. IEEE J. Sel. Topics Quantum Electron 20, 405–416 (2014).
Smit, M. et al. An introduction to InPbased generic integration technology. Semicond. Sci. Technol. 29, 083001 (2014).
Zhang, P. et al. Referenceframeindependent quantumkeydistribution server with a telecom tether for an onchip client. Phys. Rev. Lett. 112, 130501 (2014).
Vest, G. et al. Design and evaluadtion of a handheld quantum key distribution sender module. IEEE J. Sel. Topics Quantum Electron 21, 6600607 (2014).
Sibson, P. et al. Chipbased quantum key distribution. Preprint at arXiv:1509.00768 (2015).
Ma, C. et al. Integrated silicon photonic transmitter for polarizationencoded quantum key distribution. Optica (in press). Preprint online available at https://arxiv.org/abs/1606.04407.
Takesue, H. et al. Differential phase shift quantum key distribution experiment over 105 km fibre. New J. Phys. 7, 232 (2005).
Nambu, Y., Yoshino, K. & Tomita, A. Quantum encoder and decoder for practical quantum key distribution using a planar lightwave circuit. J. Mod. Opt. 55, 1953–1970 (2008).
Ziebell, M. et al. CLEO/Europe (EQEC, Munich, Germany, 2015).
BechmannPasquinucci, H. & Tittel, W. Quantum cryptography using larger alphabets. Phys. Rev. A 61, 062308 (2000).
Bourennane, M., Karlsson, A. & Björk, G. Quantum key distribution using multilevel encoding. Phys. Rev. A 64, 012306 (2001).
Cerf, N. J., Bourennane, M., Karlsson, A. & Gisin, N. Security of quantum key distribution using dlevel systems. Phys. Rev. Lett. 88, 127902 (2002).
Zhang, L., Silberhorn, C. & Walmsley, I. A. Secure quantum key distribution using continuous variables of single photons. Phys. Rev. Lett. 100, 110504 (2008).
Zhang, Z., Mower, J., Englund, D., Wong, F. N. C. & Shapiro, J. H. Unconditional security of timeenergy entanglement quantum key distribution using dualbasis interferometry. Phys. Rev. Lett. 112, 120506 (2014).
Zhong, T. et al. Photonefficient quantum key distribution using timeenergy entanglement with highdimensional encoding. New J. Phys. 17, 022002 (2015).
Mirhosseini, M. et al. Highdimensional quantum cryptography with twisted light. New J. Phys. 17, 033033 (2015).
Etcheverry, S. et al. Quantum key distribution session with 16dimensional photonic states. Sci. Rep. 3, 2316 (2013).
Sasaki, T., Yamamoto, Y. & Koashi, M. Practical quantum key distribution protocol without monitoring signal disturbance. Nature 509, 475–478 (2014).
Guan, J. Y. et al. Experimental passive roundrobin differential phaseshift quantum key distribution. Phys. Rev. Lett. 114, 180502 (2015).
Takesue, H., Sasaki, H., Tamaki, K. & Koashi, M. Experimental quantum key distribution without monitoring signal disturbance. Nat. Photon. 9, 827—831 (2015).
Wang, S. et al. Experimental demonstration of quantum key distribution without signal disturbance monitoring. Nat. Photon. 9, 832–836 (2015).
Li, Y. H. et al. Experimental roundrobin differential phaseshift quantum key distribution. Phys. Rev. A 93, 030302(R) (2016).
Mizutani, A., Imoto, N. & Tamaki, K. Robustness of roundrobin differential phaseshift quantum key distribution protocol against source flaws. Phys. Rev. A 92, 060303 (2015).
Zhao, Y., Fung, C.H. F., Qi, B., Chen, C. & Lo, H.K. Quantum hacking: experimental demonstration of timeshift attack against practical quantumkeydistribution systems. Phys. Rev. A 78, 042333 (2008).
Lydersen, L. et al. Hacking commercial quantum cryptography systems by tailored bright illumination. Nat. Photon. 4, 686–689 (2010).
Xu, F., Qi, B. & Lo, H.K. Experimental demonstration of phaseremapping attack in a practical quantum key distribution system. New J. Phys. 12, 113026 (2010).
Mayers, D. & Yao, A. Quantum cryptography with imperfect apparatus. in Proceedingsof the 39th Annual Symposium on Foundations of Computer Science, 1998. 503–509 (IEEE, 1998).
Can, A. et al. Deviceindependent security of quantum cryptography against collective attacks. Phys. Rev. Lett. 98, 230501 (2007).
Braunstein, S. L. & Pirandola, S. Sidechannelfree quantum key distribution. Phys. Rev. Lett. 108, 130502 (2012).
Shalm, L. K. et al. A strong loopholefree test of local realism. Phys. Rev. Lett. 115, 250402 (2015).
Giustina, M. et al. A significantloopholefree test of Bell’s theorem with entangled photons. Phys. Rev. Lett. 115, 250401 (2015).
Biham, E., Huttner, B. & Mor, T. Quantum cryptographic network based on quantum memories. Phys. Rev. A 54, 2651 (1996).
Inamori, H. Security of practical timereversed EPR quantum key distribution. Algorithmica 34, 340 (2002).
Curty, M. et al. Finitekey analysis for measurementdeviceindependent quantum key distribution. Nat. Commun. 5, 3732 (2014).
Lim, C. C. W., Portmann, C., Tomamichel, M., Renner, R. & Gisin, N. Deviceindependent quantum key distribution with local Bell test. Phys. Rev. X 3, 031006 (2013).
Tang, Y.L. et al. Measurementdeviceindependent quantum key distribution over 200 km. Phys. Rev. Lett. 113, 190501 (2014).
Yin, H.L. et al. Measurement device independent quantum key distribution over 404 km optical fibre. Preprint at arXiv:1606.06821 (2016).
Tang, Y.L. et al. Field test of measurementdeviceindependent quantum key distribution. IEEE J. Sel. T. Quantum Electron. 21, 6600407 (2014).
Valivarthi, R. et al. Measurementdeviceindependent quantum key distribution: from idea towards application. J. Mod. Opt. 62, 1141–1150 (2015).
Tang, Y.L. et al. Measurementdeviceindependent quantum key distribution over untrustful metropolitan network. Phys. Rev. X 6, 011024 (2015).
Comandar, L. C. et al. Quantum cryptography without detector vulnerabilities using opticallyseeded lasers. Nat. Photon. 10, 312–315 (2016).
Xu, F., Curty, M., Qi, B., Qian, L. & Lo, H.K. Discrete and continuous variables for measurementdeviceindependent quantum cryptography. Nat. Photon. 9, 772 (2015).
Yuan, Z.L. et al. Interference of short optical pulses from independent gainswitched laser diodes for quantum secure communications. Phys. Rev. Applied 2, 064006 (2014).
Tamaki, K., Lo, H.K., Fung, C.H. F. & Qi, B. Phase encoding schemes for measurementdeviceindependent quantum key distribution with basisdependent flaw. Phys. Rev. A 85, 042307 (2012).
González, P. et al. Quantum key distribution with untrusted detectors. Phys. Rev. A 92, 022337 (2015).
Lim, C. C. W. et al. Detectordeviceindependent quantum key distribution. Appl. Phys. Lett. 105, 221112 (2014).
Cao, W.F. et al. Highly efficient quantum key distribution immune to all detector attacks. Preprint at arXiv:1410.2928v1 (2014).
Kim, Y.H. Singlephoton twoqubit entangled states: Preparation and measurement. Phys. Rev. A 67, 040301(R) (2003).
Gisin, N., Fasel, S., Kraus, B., Zbinden, H. & Ribordy, G. Trojanhorse attacks on quantumkeydistribution systems. Phys. Rev. A 73, 022320 (2006).
Qi, B. Trustworthiness of detectors in quantum key distribution with untrusted detectors. Phys. Rev. A 91, 020303(R) (2015).
Liang, W.Y. et al. Simple implementation of quantum key distribution based on singlephoton bell state measurement. Phys. Rev. A 92, 012319 (2015).
Pirandola, S. et al. Highrate measurementdeviceindependent quantum cryptography. Nat. Photon. 9, 397–402 (2015).
Li, Z., Zhang, Y.C., Xu, F., Peng, X. & Guo, H. Continuousvariable measurementdeviceindependent quantum key distribution. Phys. Rev. A 89, 052301 (2014).
Ma, X.C., Sun, S.H., Jiang, M.S., Gui, M. & Liang, L.M. Gaussianmodulated coherentstate measurementdeviceindependent quantum key distribution. Phys. Rev. A 89, 042335 (2014).
Gehring, T. et al. Implementation of continuousvariable quantum key distribution with composable and onesideddeviceindependent security against coherent attacks. Nat. Commun. 6, 8795 (2015).
Pirandola, S. et al. Reply to 'Discrete and continuous variables for measurementdeviceindependent quantum cryptography'. Nat. Photon. 9, 773 (2015).
Yin, Z.Q. et al. Measurementdeviceindependent quantum key distribution with uncharacterized qubit sources. Phys. Rev. A 88, 062322 (2013).
Yin, Z.Q. et al. Mismatchedbasis statistics enable quantum key distribution with uncharacterized qubit sources. Phys. Rev. A 90, 052319 (2014).
Barnett, S. M., Huttner, B. & Phoenix, S. Eavesdropping strategies and rejecteddata protocols in quantum cryptography. J. Mod. Opt. 40, 2501 (1993).
Dušek, M., Jahma, M. & Lütkenhaus, N. Unambiguous state discrimination in quantum cryptography with weak coherent states. Phys. Rev. A 62, 022306 (2000).
Xu, F. et al. Experimental quantum key distribution with source flaws. Phys. Rev. A 92, 032305 (2015).
Mizutani, A., Curty, M., Lim, C. C. W., Imoto, N. & Tamaki, K. Finitekey security analysis of quantum key distribution with imperfect light sources. New J. Phys. 17, 093011 (2015).
Cao, Z., Zhang, Z., Lo, H.K. & Ma, X. Discretephaserandomized coherent state source and its application in quantum key distribution. New J. Phys. 17, 053014 (2015).
Yuan, Z. L. et al. Robust random number generation using steadystate emission of gainswitched laser diodes. Appl. Phys. Lett. 104, 261112 (2014).
Yuan, Z. L. et al. A directly phasemodulated light source. Phys. Rev. X 6, 031044 (2016).
Jain, N. et al. Trojanhorse attacks threaten the security of practical quantum cryptography. New J. Phys. 16, 123030 (2014).
Jain, N. et al. Risk analysis of trojanhorse attacks on practical quantum key distribution systems. IEEE J. Sel. Topics Quantum Electron 21, 6600710 (2015).
Stiller, B. et al. in 2015 Conference on Lasers and ElectroOptics (CLEO) (ed. Goldwasser, S.) (Optical Society of America, 2015).
Lucamarini, M. et al. Practical security bounds against the Trojanhorse attack in quantum key distribution. Phys. Rev. X 5, 031030 (2015).
Tang, Z., Wei, K., Bedroya, O., Qian, L. & Lo, H.K. Experimental measurementdeviceindependent quantum key distribution with imperfect sources. Phys. Rev. A 93, 042308 (2016).
Paul, C. K. in Advances in Cryptology—CRYPTO 1996 104–113 (Springer, 1996).
Kocher, P., Jaffe, J. & Jun, B. in Advances in Cryptology—CRYPTO 1999 388–397 (Springer, 1999).
Genkin, D., Shamir, A. & Tromer, E. in Advances in Cryptology—CRYPTO 2014 444–461 (Springer, 2014).
Sasaki, M. et al. Field test of quantum key distribution in the Tokyo QKD network. Opt. Express 19, 10387 (2011).
Northup, T. E. & Blatt, R. Quantum information transfer using photons. Nat. Photon. 8, 356 (2014).
Bussières, F. et al. Quantum teleportation from a telecomwavelength photon to a solidstate quantum memory. Nat. Photon. 8, 775 (2014).
Munro, W. J., Stephens, A. M., Devitt, S. J., Harrison, K. A. & Nemoto, K. Quantum communication without the necessity of quantum memories. Nat. Photon. 6, 777–781 (2012).
Azuma, K., Tamaki, K. & Lo, H.K. Allphotonic quantum repeaters. Nat. Commun. 6, 6787 (2015).
Buttler, W. T. et al. Daylight quantum key distribution over 1.6 km. Phys. Rev. Lett. 84, 5652 (2000).
Nauerth, S. et al. Airtoground quantum communication. Nat. Photon. 7, 382–386 (2013).
Wang, J.Y. et al. Direct and fullscale experimental verifications towards groundsatellite quantum key distribution. Nat. Photon. 7, 387–393 (2013).
Vallone, G. et al. Experimental satellite quantum communications. Phys. Rev. Lett. 115, 040502 (2015).
Meyers, R. E. in Advanced Free Space Optics (FSO) 343–387 (Springer, 2015).
Elser, D. et al. in IEEE ICSOS 2015, (New Orleans, USA, 2015).
Bourgoin, J. P. et al. Freespace quantum key distribution to a moving receiver. Opt. Express 23, 33437–33447 (2015).
Usenko, V. C. et al. Entanglement of Gaussian states and the applicability to quantum key distribution over fading channels. New J. Phys. 14, 093048 (2012).
Heim, B. et al. Atmospheric continuousvariable quantum communication. New J. Phys. 16, 113018 (2014).
Usenko, V. C. & Filip, R. Feasibility of continuousvariable quantum key distribution with noisy coherent states. Phys. Rev. A 81, 022318 (2010).
Weedbrook, C., Pirandola, S., Lloyd, S. & Ralph, T. C. Quantum cryptography approaching the classical limit. Phys. Rev. Lett. 105, 110501 (2010).
Weedbrook, C., Pirandola, S. & Ralph, T. C. Continuousvariable quantum key distribution using thermal states. Phys. Rev. A 86, 022318 (2012).
Broadbent, A. & Schaffner, C. Quantum cryptography beyond quantum key distribution. Des. Codes Cryptogr. 78, 351–382 (2016).
Mayers, D. Unconditionally secure quantum bit commitment is impossible. Phys. Rev. Lett. 78, 3414–3417 (1997).
Lo, H.K. & Chau, H. F. Is quantum bit commitment really possible? Phys. Rev. Lett. 78, 3410–3413 (1997).
Lunghi, T. et al. Practical relativistic bit commitment. Phys. Rev. Lett. 115, 030502 (2015).
Cleve, R., Gottesman, D. & Lo, H.K. How to share a quantum secret. Phys. Rev. Lett. 83, 648–651 (1999).
Hillery, M., Bužek, V. & Berthiaume, A. Quantum secret sharing. Phys. Rev. A 59, 1829–1834 (1999).
Bell, B. A. et al. Experimental demonstration of graphstate quantum secret sharing. Nat. Commun. 5, 5480 (2014).
Berlin, G. et al. Flipping quantum coins. Nat. Commun. 2, 561 (2011).
Pappa, A. et al. Experimental plug and play quantum coin flipping. Nat. Commun. 5, 3717 (2014).
Buhrman, H., Cleve, R., Watrous, J. & Wolf, R. D. Quantum fingerprinting. Phys. Rev. Lett. 87, 167902 (2001).
Xu, F. et al. Experimental quantum fingerprinting. Nat. Commun. 6, 8735 (2015).
Gottesman, D. & Chuang, I. Quantum digital signatures. Preprint at quantph/0105032 (2001).
Donaldson, R. J. et al. Experimental demonstration of kilometerrange quantum digital signatures. Phys. Rev. A 93, 012329 (2016).
Broadbent, A., Fitzsimons, J. & Kashefi, E. in Proceedings of the 50th Annual Symposium on Foundations of Computer Science 517–526 (IEEE, 2009).
Barz, S. et al. Experimental demonstration of blind quantum computing. Science 335, 303 (2012).
Lau, H.K. & Lo, H.K. Insecurity of positionbased quantumcryptography protocols against entanglement attacks. Phys. Rev. A 83, 012322 (2011).
Buhrman, H. et al. Positionbased quantum cryptography: Impossibility and constructions. SIAM J. Comput. 43, 150–178 (2014).
Chakraborty, K. & Leverrier, A. Practical positionbased quantum cryptography. Phys. Rev. A 92, 052304 (2015).
Wehner, S., Curty, M., Schaffner, C. & Lo, H.K. Implementation of twoparty protocols in the noisystorage model. Phys. Rev. A 81, 052336 (2010).
Lam, P.K. & Ralph, T. Quantum cryptography: Continuous improvement. Nat. Photon. 7, 350 (2013).
Sajeed, S, Huang, A, Sun, S, Xu, F, Makarov, V & Curty, M. Insecurity of detectordeviceindependent quantum key distribution. https://arxiv.org/abs/1607.05814 (2016).
Barrett, J., Colbeck, R. & Kent, A. Memory attacks on deviceindependent quantum cryptography. Phys. Rev. Lett. 110, 010503 (2013).
Acknowledgements
We acknowledge helpful comments from many colleagues including Romain Alléaume, HoiFung Chau, Marcos Curty, Philippe Grangier, Anthony Leverrier, Charles Ci Wen Lim, Marco Lucamarini, Xiongfeng Ma, Joyce Poon, Li Qian, Kiyoshi Tamaki and Feihu Xu. We thank our colleagues including Ping Koy Lam, Vikas Anant, Jessie QinDregely, Chris Erven, Masato Koashi, Philip Sibson, Mark Thompson and Qiang Zhang for allowing us to reproduce some of their figures. We thank Warren Raye of Nature Partner Journals for securing the permission for reproductions of figures from various publishers. We acknowledge financial support from NSERC, CFI, ORF, the US Office of Naval Research (ONR), the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory (managed by UTBattelle LLC for the US Department of Energy), the City of Paris, the French National Research Agency, the IledeFrance Region, the FranceUSA Partner University Fund, and the Commissioned Research of National Institute of Information and Communications Technology (NICT), Japan.
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Owing to the employments and consulting activities of some of the authors, they have financial interests in the commercial applications of quantum key distribution.
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Diamanti, E., Lo, HK., Qi, B. et al. Practical challenges in quantum key distribution. npj Quantum Inf 2, 16025 (2016). https://doi.org/10.1038/npjqi.2016.25
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DOI: https://doi.org/10.1038/npjqi.2016.25
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