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Most security proofs of quantum key distribution (QKD) assume that there is no unwanted information leakage about the state preparation process. However, this assumption is impossible to guarantee in practice, as QKD systems can leak information to the channel due to device imperfections or the active action of an eavesdropper. Here, we solve this pressing issue by introducing a security proof in the presence of information leakage from all state preparation settings for arguably the most popular QKD scheme, namely the decoy-state BB84 protocol. The proof requires minimal experimental characterization, as only a single parameter related to the isolation of the source needs to be determined, thus providing a clear path for bridging the gap between theory and practice. Moreover, if information about the state of the side channels is available, this can be readily incorporated into the analysis to further improve the resulting performance., Comment: 18 pages, 10 figures

A prevalent issue in practical applications of quantum key distribution (QKD) is the emergence of correlations among the emitted signals. Although recent works have proved the security of QKD in the presence of this imperfection, they rest on the premise that pulse correlations are of finite length. However, this assumption is not necessarily met in practice, since the length of these correlations could be potentially unbounded. Indeed, the first emitted pulse could be correlated with the last one, even if very faintly. Still, intuitively, there should exist a pulse separation threshold after which these correlations become so small as to be essentially negligible, rendering them inconsequential from a security standpoint. Building on this insight, we introduce a general formalism designed to extend existing security proofs to the practically relevant scenario in which pulse correlations have an unbounded length. This approach significantly enhances the applicability of these proofs and the robustness of QKD's implementation security.

Quantum key distribution (QKD) can theoretically achieve the Holy Grail of cryptography, information-theoretic security against eavesdropping. However, in practice, discrepancies between the mathematical models assumed in security proofs and the actual functioning of the devices used in implementations prevent it from reaching this goal. Device-independent QKD is currently not a satisfactory solution to this problem, as its performance is extremely poor and most of its security proofs assume that the user devices leak absolutely no information to the outside. On the other hand, measurement-device-independent (MDI) QKD can guarantee security with arbitrarily flawed receivers while achieving high performance, and the remaining challenge is ensuring its security in the presence of source imperfections. So far, all efforts in this regard have come at a price; some proofs are suitable only for particular source imperfections, while others severely compromise the system's performance, i.e., its communication speed and distance. Here, we overcome these crucial problems by presenting a security proof in the finite-key regime against coherent attacks that can incorporate general encoding imperfections and side channels while achieving much higher performances than previous approaches. Moreover, our proof requires minimal state characterization, which facilitates its application to real-life implementations., Comment: Main text: 9 pages, 3 figures. Supplementary information: 63 pages, 12 figures. v2: Added many improvements and extensions to the security proof, including: (1) analysis in finite-key regime, (2) inclusion of measurement-device-independent type protocols, (3) consideration of sources that emit weak coherent pulses, (4) consideration of sources that introduce correlations across consecutive pulses

Decoy-state quantum key distribution (QKD) is undoubtedly the most efficient solution to handle multi-photon signals emitted by laser sources, and provides the same secret key rate scaling as ideal single-photon sources. It requires, however, that the phase of each emitted pulse is uniformly random. This might be difficult to guarantee in practice, due to inevitable device imperfections and/or the use of an external phase modulator for phase randomization, which limits the possible selected phases to a finite set. Here, we investigate the security of decoy-state QKD with arbitrary, continuous or discrete, non-uniform phase randomization, and show that this technique is quite robust to deviations from the ideal uniformly random scenario. For this, we combine a novel parameter estimation technique based on semi-definite programming, with the use of basis mismatched events, to tightly estimate the parameters that determine the achievable secret key rate. In doing so, we demonstrate that our analysis can significantly outperform previous results that address more restricted scenarios.

The Bennett-Brassard 1984 (BB84) protocol is the most widely implemented quantum key distribution (QKD) scheme. However, despite enormous theoretical and experimental efforts in the past decades, the security of this protocol with imperfect sources has not yet been rigorously established. In this work, we address this shortcoming and prove the security of the BB84 protocol in the presence of multiple source imperfections, including state preparation flaws and side channels, such as Trojan-horse attacks, mode dependencies and classical correlations between the emitted pulses. To do so, we consider a modified BB84 protocol that exploits the basis mismatched events, which are often discarded in standard security analyses of this scheme; and employ the reference technique, a powerful mathematical tool to accommodate source imperfections in the security analysis of QKD. Moreover, we compare the achievable secret-key rate of the modified BB84 protocol with that of the three-state loss-tolerant protocol, and show that the addition of a fourth state, while redundant in ideal conditions, significantly improves the estimation of the leaked information in the presence of source imperfections, resulting in a better performance. This work demonstrates the relevance of the BB84 protocol in guaranteeing implementation security, taking us a step further towards closing the existing gap between theory and practice of QKD.

The performance of quantum key distribution (QKD) is severely limited by multiphoton emissions, due to the photon-number-splitting attack. The most efficient solution, the decoy-state method, requires that the phases of all transmitted pulses are independent and uniformly random. In practice, however, these phases are often correlated, especially in high-speed systems, which opens a security loophole. Here, we address this pressing problem by providing a security proof for decoy-state QKD with correlated phases that offers key rates close to the ideal scenario. Our work paves the way towards high-performance secure QKD with practical laser sources, and may have applications beyond QKD., Comment: 22 pages, 1 figure. v3: Updated to Accepted Manuscript

The core of security proofs of quantum key distribution (QKD) is the estimation of a parameter that determines the amount of privacy amplification that the users need to apply in order to distill a secret key. To estimate this parameter using the observed data, one needs to apply concentration inequalities, such as random sampling theory or Azuma's inequality. The latter can be straightforwardly employed in a wider class of QKD protocols, including those that do not rely on mutually unbiased encoding bases, such as the loss-tolerant (LT) protocol. However, when applied to real-life finite-length QKD experiments, Azuma's inequality typically results in substantially lower secret-key rates. Here, we propose an alternative security analysis of the LT protocol against general attacks, for both its prepare-and-measure and measure-device-independent versions, that is based on random sampling theory. Consequently, our security proof provides considerably higher secret-key rates than the previous finite-key analysis based on Azuma's inequality. This work opens up the possibility of using random sampling theory to provide alternative security proofs for other QKD protocols., Comment: 24 pages, 5 figures. v2: Corrected a technical issue; bold math was not displayed properly in Appendix B

Twin-field (TF) quantum key distribution (QKD) can overcome fundamental secret-key-rate bounds on point-to-point QKD links, allowing us to reach longer distances than ever before. Since its introduction, several TF-QKD variants have been proposed, and some of them have already been implemented experimentally. Most of them assume that the users can emit weak coherent pulses with a continuous random phase. In practice, this assumption is often not satisfied, which could open up security loopholes in their implementations. To close this loophole, we propose and prove the security of a TF-QKD variant that relies exclusively on discrete phase randomisation. Remarkably, our results show that it can also provide higher secret-key rates than counterpart protocols that rely on continuous phase randomisation.

Memory-assisted quantum key distribution (MA-QKD) systems are among novel promising solutions that can improve the key-rate scaling with channel loss. By using a middle node with quantum storage and measurement functionalities, they offer the same key-rate scaling with distance as a single-node quantum repeater. However, the distance at which they can surpass the nominal key rate of repeaterless systems, in terms of bits per second, is typically long, owing to the efficiency and/or interaction time issues when one deals with quantum memories. This crossover distance can be a few hundred kilometres, for instance, when one relies on the exchange of infinitely many key bits for the key-rate analysis. In a realistic setup, however, we should account for the finite-key effects in our analysis. Here, we show that accounting for such effects would actually favour MA-QKD setups, by reducing the crossover distance to the regime where realistic implementations can take place. We demonstrate this by rigorously analysing a decoy-state version of MA-QKD, in the finite-key regime, using memory parameters already achievable experimentally. This provides us with a better understanding of the advantages and challenges of working with memory-based systems., Comment: 23 pages, 4 figures. v2: Updated to accepted version

Quantum key distribution (QKD) offers a reliable solution to communication problems that require long-term data security. For its widespread use, however, the rate and reach of QKD systems must be improved. Twin-field (TF) QKD is a step forward toward this direction, with early demonstrations suggesting it can beat the current rate-versus-distance records. A recently introduced variant of TF-QKD is particularly suited for experimental implementation, and has been shown to offer a higher key rate than other variants in the asymptotic regime where users exchange an infinite number of signals. Here, we extend the security of this protocol to the finite-key regime, showing that it can overcome the fundamental bounds on point-to-point QKD with around $10^{10}$ transmitted signals. Within distance regimes of interest, our analysis offers higher key rates than those of alternative variants. Moreover, some of the techniques we develop are applicable to the finite-key analysis of other QKD protocols., Comment: 26 pages, 5 figures. v2: major changes on subsection "Concentration inequality for sums of dependent random variables", minor changes elsewhere. v3: Changes on subsection "Concentration inequality for sums of dependent random variables", to use the newest version of the inequality in Ref. [38]. Minor changes in citations elsewhere. v4: Fixed wrong citation numbers in graph legends

Quantum communication is rapidly gaining popularity due to its high security and technological maturity. However, most implementations are limited to just two communicating parties (users). Quantum communication networks aim to connect a multitude of users. Here we present a fully connected quantum communication network on a city wide scale without active switching or trusted nodes. We demonstrate simultaneous and secure connections between all 28 pairings of 8 users. Our novel network topology is easily scalable to many users, allows traffic management features and minimises the infrastructure as well as the user hardware needed., Comment: 16 pages, 9 figures, 3 tables. Corrected typos, updated references

We propose a low-complexity near-optimal wavelength allocation technique for quantum key distribution access networks that rely on wavelength division multiple access. Such networks would allow users to send quantum and classical signals simultaneously on the same optical fiber infrastructure. Users can be connected to the access network via optical wireless or wired links. We account for the background noise present in the environment, as well as the Raman noise generated by classical channels, and calculate the secret key generation rate for quantum channels in the finite-key setting. This allows us to examine the feasibility of such systems in realistic scenarios when the secret key exchange needs to be achieved in a limited time scale. Our numerical results show that, by proper choice of system parameters for this noisy system, it is possible to exchange a secret key in tens of seconds. Moreover, our proposed algorithm can enhance the key rate of quantum channels, especially in high noise and/or high loss regimes of operation.