Kiyoshi Tamaki

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.

We prove the unconditional security of the Bennett 1992 quantum key distribution protocol over lossy and noisy channel. We assume that Alice has an ideal single photon source and Bob has detectors that discriminate between single photon states on one hand and vacuum state or multiphoton states on the other hand. We use a reduction to an entanglement distillation protocol initiated by a local filtering process in our proof. The bit errors and the phase errors are correlated after the filtering, and we can bound the amount of phase errors from the observed bit errors by an estimation method involving nonorthogonal measurements.

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.

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.

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.

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 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 distil 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.

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.

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.

In most of the security proofs of continuous variable quantum key distribution (CV-QKD), except for the security proof of an entangle-based protocol by F. Furrer et. al. [Phys. Rev. Lett. 109 , 100502 (2012)], it is required that Bob’s local oscillator (LO) for homodyne or heterodyne measurements is perfectly prepared. Since Eve can freely manipulate LO transmitted from Alice to Bob in standard CV-QKD systems, this requirement cannot be met. Moreover, the requirement includes the assumption that the intensity of Bob’s LO must be infinite, which is impossible to achieve in reality. In this work, we fill the gap between a standard CV-QKD system and the existing security proofs by providing a security proof accommodating the manipulation of LO by Eve.

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.