Marcos Curty

Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.

Twin-field quantum key distribution (TF-QKD) has become a leading protocol to bring quantum communications to the national scale. The protocol requires the establishment of a shared phase and frequency reference between distant parties, which is commonly achieved by using an external reference laser in an optical injection locking (OIL) architecture. In this work, we analyze the side channels in OIL-based TF-QKD that may arise from adversarial manipulation of the various degrees of freedom of this untrusted reference beam. We experimentally demonstrate two realistic attack scenarios: fast intensity modulation of the reference laser, and additional signals embedded in the reference light exploiting wavelengths undetectable by conventional monitoring techniques. These attacks can allow a potential eavesdropper to deterministically increase the mean photon number of the sources, or circumvent the decoy-state technique, respectively. To counter these vulnerabilities, we propose practical and highly effective countermeasures that reinforce the security of TF-QKD systems without significant additional complexity or performance degradation.

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.

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.

Coherent-one-way (COW) quantum key distribution (QKD) held the promise of distributing secret keys over long distances with a simple experimental setup while being robust against the photon-number splitting attack. Indeed, there are already commercial products implementing this scheme, and long distance realizations over 300 km have been reported recently. Surprisingly enough, however, here we show that its asymptotic secret key rate scales at most quadratically with the system's transmittance, thus solving a long standing problem. This means that COW is actually inappropriate for long distance QKD transmission. This is done by deriving the optimal zero-error attack, which is a type of attack where the eavesdropper does not introduce any error, but still prevents Alice and Bob from distilling a secure key. In doing so, we also show, for instance, that all implementations of the COW scheme reported so far in the scientific literature are insecure.

The fabrication of quantum key distribution (QKD) systems typically involves several parties, thus providing Eve with multiple opportunities to meddle with the devices. As a consequence, conventional hardware and/or software hacking attacks pose natural threats to the security of practical QKD. Fortunately, if the number of corrupted devices is limited, the security can be restored by using redundant apparatuses. Here, we report on the demonstration of a secure QKD setup with optical devices and classical post-processing units possibly controlled by an eavesdropper. We implement a 1.25 GHz chip-based measurement-device-independent QKD system secure against malicious devices on both the measurement and the users' sides. The secret key rate reaches 137 bps over a 24 dB channel loss. Our setup, benefiting from high clock rate, miniaturized transmitters and a cost-effective structure, provides a promising solution for widespread applications requiring uncompromising communication security.

The twin-field (TF) quantum key distribution (QKD) protocol and its variants are highly attractive because they can beat the well-known fundamental limit of secret key rate for point-to-point (point-to-point bound) QKD without quantum repeaters. In this paper, we perform a proof-of-principle experimental demonstration of TF-QKD based on the protocol proposed by Curty et al., which removes the need for post-selection on the matching of a global phase from the original TF-QKD. Furthermore, we employ a Sagnac loop structure to overcome the major difficulty in the practical implementation of TF-QKD, namely, the need to stabilize the phase of the quantum state over kilometers of fiber. The experimental results show that the secret key rate of TF-QKD at high loss region can surpass the point-to-point bound of QKD with current technology.

Phase randomization is essential for the security of practical quantum key distribution (QKD) systems. Commonly, implementations rely on laser sources (either actively phase-randomized, or gain-switched). However, at high repetition rates these show correlations, which can ultimate compromise security and performance. We present a 1.25 GHz fully phase-randomized QKD source based on a super luminescent diode (SLED) operating in the C-band as a compact and cost-effective alternative. The source generates ∼ 100 ps optical pulses with 400 ps time-bin separation, compatible with high-speed time-bin encoding. Interferometric measurements demonstrate > 99% visibility between adjacent time bins, confirming strong first-order coherence within a qubit, while the spontaneous-emission-driven nature of the SLED ensures intrinsic pulse to pulse phase randomization. The broadband architecture further enables operation across multiple ITU channels, supporting wavelength-multiplexed QKD from a single emitter. This work establishes a scalable SLED-based platform for high-speed time-bin QKD systems.

The performance of quantum key distribution (QKD) heavily depends on statistical inference. For a broad class of protocols, the central statistical task is a random sampling problem, customarily addressed using exponential tail bounds on the hypergeometric distribution. Here, we provide an alternative solution for this task of unprecedented tightness among QKD security analyses. As a by-product, confidence intervals for the average of non-identical Bernoulli parameters follow too. These naturally fit in statistical analyses of decoy-state QKD and also outperform standard tools. Lastly, we show that, in a vast parameter regime, the use of tail bounds is not enforced because the cumulative mass function of the hypergeometric distribution is accurately computable. This sharply decreases the minimum block sizes necessary for QKD, and reveals the tightness of our simple analytical bounds when moderate-to-large blocks are considered. Mannalath, V., Zapatero, V., & Curty, M. (2024). Sharp finite statistics for quantum key distribution. arXiv:2410.04095 (2024). Currently under consideration in Phys. Rev. Lett. (second round of revision).

Numerical security proofs offer a versatile approach for evaluating the secret-key generation rate of quantum key distribution (QKD) protocols. However, existing methods typically require perfect source characterization, which is unrealistic in practice due to the presence of inevitable encoding imperfections and side channels. In this paper, we introduce a novel security proof technique based on semidefinite programming that can evaluate the secret-key rate for both prepare-and-measure and measurement-device-independent QKD protocols when only partial information about the emitted states is available, significantly improving the applicability and practical relevance compared to existing numerical techniques. We demonstrate that our method can outperform current analytical approaches addressing partial state characterization in terms of achievable secret-key rates, particularly for protocols with non-qubit encoding spaces. This represents a significant step towards bridging the gap between theoretical security proofs and practical QKD implementations.

Bandwidth-limited devices in the transmitter of fast QKD implementations cause pulse correlations that leak information about previous setting choices. To take them into account in the existing security proofs, a measure of their strengths is needed. This is experimentally challenging, especially for long-range correlations, which are not experimentally accessible. In this work, we propose a new characterization method that exploits a linear model of the modulation devices. We show that this model predicts an upper bound for arbitrary order correlations that makes their characterization possible. We also present experimental results using the proposed method. In doing so, we can retrieve security even in the presence of arbitrary long correlations, with similar performance to classical security proofs.

Current implementations of quantum key distribution (QKD) typically rely on prepare-and-measure (P&M) schemes. Unfortunately, these implementations are not completely secure, unless security proofs fully incorporate all imperfections of real devices. So far, existing proofs have primarily focused on imperfections of either the light source or the measurement device. In this work, we establish a security proof for the loss-tolerant P&M QKD protocol that incorporates imperfections in both the source and the detectors. Specifically, we demonstrate the security of this scheme when the emitted states deviate from the ideal ones and Bob’s measurement device does not meet the basis-independent detection efficiency condition. Furthermore, we conduct an experiment to characterise the detection efficiency mismatch of commercial single-photon detectors as a function of the polarisation state of the input light, and determine the expected secret key rate in the presence of state preparation flaws when using such detectors. Our work provides a way towards guaranteeing the security of actual implementations of widely deployed P&M QKD.

Chip-based quantum key distribution (QKD) systems offer improved efficiency but may also introduce previously unrecognized security vulnerabilities. In this work, we identify and experimentally characterize cross-polarization-intensity (CPI) correlations in a real-world chip-based QKD system. Moreover, we introduce a security analysis that incorporates CPI correlations and apply it to evaluate the performance of an integrated high-speed QKD system. Our results emphasize the need for rigorous security assessments in chip-based QKD implementations.

Typical security proofs of quantum key distribution (QKD) require that the emitted signals are independent and identically distributed. In practice, however, this assumption is not met because intrinsic device flaws inevitably introduce correlations between the emitted signals. Although analyses addressing this issue have been recently proposed, they only consider a restrictive scenario in which the correlations have a finite and known maximum length that is much smaller than the total number of emitted signals. While it is expected that the magnitude of the correlations decreases as the pulse separation increases, the assumption that this magnitude is exactly zero after a certain point does not seem to have any physical justification. Concerningly, this means that existing analyses cannot guarantee the security of current QKD implementations. Here, we solve this pressing problem by developing a general framework that can handle pulse correlations of unbounded length. Our framework allows us to directly use existing proofs addressing this imperfection without the need to construct them from scratch, thus reestablishing the security of QKD in a simple and versatile manner.

Quantum key distribution (QKD) has raised as an attractive alternative to classical cryptography due to its security being provided by quantum mechanics rather than relying on algorithms that could potentially be broken in the future, rendering current communications insecure. However, many of the security proofs rely on assumptions that may not agree with reality, for instance, device imperfections can open loopholes that could potentially be exploited by a malicious party in order to extract part, if not all, of the secret key.

Quantum Key Distribution (QKD) is a crucial technology for secure communication, relying on the principles of quantum mechanics. The security of QKD protocols is often analyzed by bounding the probability of a "failure" during the parameter estimation step. This failure probability is typically addressed using tail bounds on the hypergeometric distribution. However, existing methods can sometimes be conservative, leading to inefficiencies. In this work, we present an alternative approach that provides a more refined bound by exploiting a simple yet effective link between hypergeometric and binomial random variables.

Recently, different modulator-free decoy-state quantum key distribution transmitters have been proposed. Among their advantages, they are essentially immune to information leakage, including that potentially induced by an adversary via e.g. a Trojan-horse attack. However, practical implementations of these transmitters emit, in addition to the desired signals, some extra pulses that are not used as quantum carriers, but still may contain sensitive information about the intensity and bit/basis encoding of the signals. This unwanted pulses can be actively blocked with an intensity modulator (or an optical switch), but the extinction ratio of these devices is always finite, and thus it is still crucial to account for the residual amount of information leakage at the security-proof level. In this work, we analyze the security of these transmitters and evaluate their performance in the presence of this kind of inherent information leakage. We find that the secret-key rate of the protocol is severely affected when the information leakage is not sufficiently attenuated, which highlights the importance of accounting for such type of imperfections.

A crucial assumption in most quantum key distribution (QKD) security proofs, is that no information about the selected settings is leaked to the channel. A secure space around the users' devices is usually required to ensure both parties can generate and handle classical data securely. However, this condition is not feasible in practice, since the devices usually leak some information passively, and an eavesdropper could even run a Trojan horse attack (THA) by injecting bright light into the QKD apparatuses, causing an active leak of information. In this paper, we present the first security proof for a decoy state protocol that considers an arbitrary leakage from every setting selected in the source due to passive or active information leakage. Furthermore, we apply our security proof to various cases of practical interest and we analyze the effectiveness of placing an extra phase modulator in the source to improve the secret key rate. Our analysis is also experimentally friendly, as it only requires one parameter to encapsulates all side-channel imperfections. We believe that our results constitute a vital step in closing the existing gap between theory and implementation in QKD.

The decoy-state method is a prominent approach to enhance the performance of quantum key distribution (QKD) systems that operate with weak coherent laser sources. Current experimental decoy-state QKD setups increase their secret key rate by raising the repetition rate of the transmitter, which can lead to correlations between subsequently emitted optical pulses. This phenomenon leaks information about the encoding settings, including the intensities of the generated signals, thus invalidating a basic premise of decoy-state QKD. Here, we experimentally characterize intensity correlations between the nearest-neigbouring optical pulses in two commercial prototypes of decoy-state BB84 QKD systems and show that they significantly reduce the asymptotic key rate. In addition, we study intensity correlations between pulses spaced further apart (higher-order correlations) and find that, in contrast to what has been conjectured, their impact on the intensity of the generated signals can be much higher than that of the nearest-neighbour (first-order) correlations.

Quantum key distribution (QKD) promises theoretically unbreakable encryption by exploiting the principles of quantum mechanics. However, the security of real-world implementations is compromised by inevitable device imperfections, unless these are accounted for in the security proof. In this work, we introduce an innovative and powerful security proof framework that guarantees robustness against all practical source imperfections while maintaining high performances, thereby significantly bridging the gap between the theoretical promise and practical realization of QKD. In combination with measurement-device-independent QKD, which closes all security loopholes related to the measurement units, our framework can guarantee an unprecedented level of implementation security.

Quantum key distribution (QKD) protocols leverage quantum mechanics to achieve information theoretically secure communication, yet real-world implementations must address experimental limitations, particularly phase correlations in weak coherent laser pulses (WCPs). High-speed gain-switching lasers, commonly used in QKD, can exhibit residual photons causing phase correlations between consecutive pulses, challenging the perfect phase randomization assumption crucial for the decoy-state BB84 protocol. Theoretical work has proposed security proofs that require knowledge of how closely each phase's probability distribution approximates uniformity, which is complex to estimate experimentally. In this study we introduce an experimental method to characterise phase correlations of any length under realistic conditions by modelling the phase generation process within the laser cavity. Additionally, we experimentally benchmark this practical routine for measuring second-order correlations using a double Michelson interferometer with tunable amplitude attenuators, allowing comprehensive characterisation of the phase generation process and accurate measurement of the phase probability distribution, thus enhancing the security of QKD systems.

Decoy-state quantum key distribution (QKD) represents nowadays the best countermeasure to attacks exploiting multi-photon emissions in realistic sources. A fundamental requirement is the uniform and independent distribution of phases of the transmitted pulses. However, this can not be true for lasers working under high-speed gain-switching conditions, as residual photons in the cavity can induce phase correlations across consecutive pulses. A security proof robust against such imperfections has been recently proposed, which requires knowledge of a parameter that quantifies how close the conditional distribution of each phase is to a uniform distribution. In this work we propose an experimental method to characterise this parameter in realistic setup conditions and we extend the application to the case of arbitrary length of correlations, aiming to enable experimental verification of the implementation security.

In decoy-state-based QKD, GHz clocked or higher frequency transmitters exhibit correlations between the intensities of succeeding pulses. As a consequence, every pulse leaks partial information about previous intensity settings to an eavesdropper, thus invalidating the fundamental principle of the decoy-states method, i.e., the independent character of the yields from the intensity settings. In this work, we present a technique that allows to incorporate arbitrary intensity correlations to the decoy-state analysis, thereby solving a pressing problem in the race towards practical high-speed QKD systems. As a side contribution, we present a non-standard derivation of the asymptotic key rate formula from the non-asymptotic one, in so revealing a largely dismissed necessary condition for the significance of the former. We discuss this condition in full detail.

There is a large gap between theory and practice in quantum key distribution (QKD) because real devices do not satisfy the assumptions required by the security proofs. We close this gap by introducing a simple and practical measurement-device-independent-QKD type of protocol, based on the transmission of coherent light, for which we prove its security against any possible imperfection and/or side channel from the quantum communication part of the QKD devices. Our approach only requires to experimentally characterize an upper bound of one single parameter for each of the pulses sent, which describes the quality of the source. Moreover, unlike device-independent (DI) QKD, it can accommodate information leakage from the users’ laboratories, which is essential to guarantee the security of QKD implementations. In this sense, its security goes beyond that provided by DI QKD, yet it delivers a secret key rate that is various orders of magnitude greater than that of DI QKD.

We present an analysis for real-life implementations of measurement-device-independent quantum-key-distribution (MDI-QKD): a general system model, an optimized finite-decoy protocol and a rigorous finite-key analysis. This is of particular interest both to researchers hoping to demonstrate MDI-QKD and to others performing non-QKD experiments involving quantum interference.