arXiv subjects

Norbert Lütkenhaus

Publications and source records attributed to Norbert Lütkenhaus.

At least 19 recordsLinked to original sources

arXiv2026

Security framework for practical quantum key distribution with imperfect devices

Practical quantum key distribution (QKD) systems inevitably exhibit imperfections in both the source and detector. At the same time, the behavior of these imperfect devices is never exactly known due to characterization uncertainty, parameter fluctuations, and potential influence by an adversary. In this work, we present a security proof for generic prepare-and-measure QKD protocols, including decoy-state BB84, with imperfect and imperfectly characterized sources and detectors using the marginal-constrained entropy accumulation theorem (MEAT). Our approach uses a sequence of proof technique independent source maps and squashing maps, yielding a very modular framework. We show that practical key rates can be achieved even when multiple imperfections are combined. More broadly, our work provides a unified foundation that avoids the need for dedicated protocol-specific arguments and can be readily extended to other protocols and device imperfections.

quant-ph↗

arXiv2026

Drone- and Vehicle-Based Quantum Key Distribution

Quantum key distribution is a point-to-point communication protocol that leverages quantum mechanics to enable secure information exchange. Commonly, the transmitter and receiver stations are at fixed locations, and the single-photon quantum states are transmitted over fiber or free space. Here, we describe a modular, platform-agnostic, quantum key distribution transmitter and receiver with reduced size, weight, and power consumption to realize a mobile quantum communication system. We deploy the system on different moving platforms, demonstrating drone-to-drone, drone-to-vehicle, and vehicle-to-vehicle quantum communication, achieving secure key rates in the finite-key regime in the range of 1.6 - 20 kbps. To prove the security of the system, we develop advanced physics models of the devices that account for non-ideal behaviors that are of greater importance in mobile platforms. The modular system can be easily upgraded to include sources of entangled photonic quantum states, which will find application in future quantum networks.

quant-ph↗

arXiv2026

Enforcing IID structure on time-bin encoded QKD protocols via coarse-graining

Many security proofs for quantum key distribution (QKD) require Bob's measurement to have a tensor-product structure across protocol rounds, with some techniques requiring the stronger independent-and-identically-distributed (IID) condition. Time-bin encoded protocols often rely on interferometers whose detector outcomes depend on the interference between optical modes from neighbouring rounds, obstructing the direct application of such proofs. We show that classical post-processing of Bob's measurement data --- specifically, discarding the outcomes of detectors sensitive to inter-round coherence --- is sufficient to recover a product measurement positive operator-valued measure (POVM) (which is IID when the same single-round setup is used in every round). Applied to the Mach-Zehnder interferometer and the IID variant of the COW detection setup, this removes the need for the additional vacuum pulse introduced in prior analyses to establish tensor product structure of the measurement POVM, recovering better key rates without placing any restriction on Eve's attack.

quant-ph↗

arXiv2026

Security proofs for practical QKD: variations, techniques, gaps, and limitations

We review the current status of security proofs for practical decoy-state Quantum Key Distribution using the BB84 protocol, focusing on optical implementations with weak coherent pulses and threshold photodetectors. The primary aim of this review is to highlight gaps in the existing literature. Such gaps may arise, for instance, from mismatches between detailed protocol specifications and proof technique elements, reliance on earlier results based on different assumptions, or protocol choices that overlook real world requirements. While substantial progress has been made, our overview draws attention to the details that still demand careful attention.

quant-ph↗

arXiv2026

Performance of BB84 without decoy states under varying announcement structures

In phase-randomized weak coherent pulse (WCP) implementations of Quantum Key Distribution (QKD) BB84 protocol, the decoy method is often used to compensate BB84's vulnerability against photon number splitting (PNS) attacks. However, this typically introduces extra complexities and requirements on experimental devices. In this paper, we are therefore interested in phase-randomized WCP implementations without the decoy method. We examine the performance of three QKD protocols with different classical announcement structures, namely BB84, SARG04, and No Public Announcement of Basis (NPAB) BB84, using numerical security proof techniques. We compare secure key rates of the three protocols in asymptotic and finite-size regimes for lossy and noisy channels. The three protocols show different relative advantages depending on the channel behaviour. Canonical BB84 shows robustness against errors and depolarization, SARG04 demonstrates resilience against high loss channels, and NPAB BB84 shows potential advantages against physical misalignment between QKD devices.

quant-ph↗

arXiv2026

Imperfect detectors for adversarial tasks with applications to quantum key distribution

Security analyses in quantum key distribution (QKD) and other adversarial quantum tasks often assume perfect device models. However, real-world implementations often deviate from these models. Thus, it is important to develop security proofs that account for such deviations from ideality. In this work, we extend the idea of squashing maps to develop a general framework for analysing imperfect threshold detectors, treating uncharacterised device parameters such as dark counts and detection efficiencies as adversarially controlled within some ranges. This approach enables a rigorous worst-case analysis with exactly characterised devices, ensuring security proofs remain valid under realistic conditions. Our results strengthen the connection between theoretical security and practical implementations by introducing a flexible framework for integrating detector imperfections into adversarial quantum protocols.

quant-ph↗

arXiv2026

A consolidated and accessible security proof for finite-size decoy-state quantum key distribution

In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.

quant-ph↗

arXiv2026

A rigorous and complete security proof of decoy-state BB84 quantum key distribution

We present a rigorous and complete security proof of the decoy-state BB84 quantum key distribution (QKD) protocol. Our analysis aims to achieve a high standard of mathematical rigour and completeness, thereby providing the necessary foundation for certification and standardization efforts. Beyond establishing the security of a specific protocol, this work develops a general and modular framework that can be readily adapted to a broad class of QKD protocols, including both prepare-and-measure and entanglement-based variants. Our framework unifies all major ingredients required for the analysis of realistic QKD protocols, including the analysis of classical authentication and classical processing, source-replacement schemes, finite-size analysis, source maps, squashing maps, and decoy-state techniques. In doing so, this work consolidates a diverse range of techniques scattered across the QKD literature into a unified formalism, representing a general and rigorous treatment of QKD security. Finally, it outlines a clear path towards incorporating practical imperfections within the same framework, thereby laying the groundwork for addressing implementation security in future analysis.

quant-ph↗

arXiv2025

Finite-Key Analysis of Quantum Key Distribution with Characterized Devices Using Entropy Accumulation

The Entropy Accumulation Theorem (EAT) was introduced to significantly improve the finite-size rates for device-independent quantum information processing tasks such as device-independent quantum key distribution (QKD). A natural question would be whether it also improves the rates for device-dependent QKD. In this work, we provide an affirmative answer to this question. We present new tools for applying the EAT in the device-dependent setting. We present sufficient conditions for the Markov chain conditions to hold as well as general algorithms for constructing the needed min-tradeoff function. Utilizing Dupuis' recent privacy amplification without smoothing result, we improve the key rate by optimizing the sandwiched Rényi entropy directly rather than considering the traditional smooth min-entropy. We exemplify these new tools by considering several examples including the BB84 protocol with the qubit-based version and with a realistic parametric downconversion source, the six-state four-state protocol and a high-dimensional analog of the BB84 protocol.

quant-ph↗

arXiv2025

Phase error rate estimation in QKD with imperfect detectors

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly characterized basis-efficiency mismatch. Our proof works by obtaining a suitable bound on the phase error rate, without requiring any new modifications to the protocol steps or hardware. It is applicable to imperfectly characterized detectors, and only requires the maximum relative difference in detection efficiencies and dark count rates of the detectors to be characterized. Moreover, our proof allows Eve to choose detector efficiencies and dark count rates in their allowed ranges in each round, thereby addressing an important problem of detector side channels. We prove security in the variable-length framework, where users are allowed to adaptively determine the length of key to be produced, and number of bits to be used for error-correction, based on observations made during the protocol. We quantitatively demonstrate the effect of basis-efficiency mismatch by applying our results to the decoy-state BB84 protocol.

quant-ph↗

arXiv2025

Finite-size analysis of prepare-and-measure and decoy-state QKD via entropy accumulation

An important goal in quantum key distribution (QKD) is the task of providing a finite-size security proof without the assumption of collective attacks. For prepare-and-measure QKD, one approach for obtaining such proofs is the generalized entropy accumulation theorem (GEAT), but thus far it has only been applied to study a small selection of protocols. In this work, we present techniques for applying the GEAT in finite-size analysis of generic prepare-and-measure protocols, with a focus on decoy-state protocols. In particular, we present an improved approach for computing entropy bounds for decoy-state protocols, which has the dual benefits of providing tighter bounds than previous approaches (even asymptotically) and being compatible with methods for computing min-tradeoff functions in the GEAT. Furthermore, we develop methods to incorporate some improvements to the finite-size terms in the GEAT, and implement techniques to automatically optimize the min-tradeoff function. Our approach also addresses some numerical stability challenges specific to prepare-and-measure protocols, which were not addressed in previous works.

quant-ph↗

arXiv2025

Quantum Chernoff divergence in advantage distillation for quantum key distribution and device-independent quantum key distribution

Device-independent quantum key distribution (DIQKD) aims to mitigate adversarial exploitation of imperfections in quantum devices, by providing an approach for secret key distillation with modest security assumptions. Advantage distillation, a two-way communication procedure in error correction, has proven effective in raising noise tolerances in both device-dependent and device-independent QKD. Previously, device-independent security proofs against IID collective attacks were developed for an advantage distillation protocol known as the repetition-code protocol, based on security conditions involving the fidelity between some states in the protocol. However, there exists a gap between the sufficient and necessary security conditions, which hinders the calculation of tight noise-tolerance bounds based on the fidelity. We close this gap by presenting an alternative proof structure that replaces the fidelity with the quantum Chernoff divergence, a distinguishability measure that arises in symmetric hypothesis testing. Working in the IID collective attacks model, we derive matching sufficient and necessary conditions for the repetition-code protocol to be secure (up to a natural conjecture regarding the latter case) in terms of the quantum Chernoff divergence, hence indicating that this serves as the relevant quantity of interest for this protocol. Furthermore, using this security condition we obtain some improvements over previous results on the noise tolerance thresholds for DIQKD. Our results provide insight into a fundamental question in quantum information theory regarding the circumstances under which DIQKD is possible.

quant-ph↗

arXiv2025

Improved finite-size effects in QKD protocols with applications to decoy-state QKD

We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks and extend it to coherent attacks using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter finite-size key rates by employing refined concentration inequalities in the acceptance testing phase. Second, we improve second-order correction terms in the key rate expression, by reducing them to scale with the number of sifted rounds rather than the total number of protocol rounds. We apply these advancements to compute finite-size key rates for a qubit and decoy-state BB84 protocol, accommodating arbitrary protocol parameters. Finally, we extend our finite-size security proof to coherent attacks and variable-length protocols and present our results for the decoy-state 4-6 protocol incorporating imperfections such as unequal intensity settings.

quant-ph↗

arXiv2024

Experimental composable key distribution using discrete-modulated continuous variable quantum cryptography

Establishing secure data communication necessitates secure key exchange over a public channel. Quantum key distribution (QKD), which leverages the principles of quantum physics, can achieve this with information-theoretic security. The discrete modulated (DM) continuous variable (CV) QKD protocol, in particular, is a suitable candidate for large-scale deployment of quantum-safe communication due to its simplicity and compatibility with standard high-speed telecommunication technology. Here, we present the first experimental demonstration of a four-state DM CVQKD system, successfully generating composable finite-size keys, secure against collective attacks over a 20 km fiber channel with 2.3 \times 10^{9} coherent quantum states, achieving a positive composable key rate of 11.04 \times 10^{-3} bits/symbol. This accomplishment is enabled by using an advanced security proof, meticulously selecting its parameters, and the fast, stable operation of the system. Our results mark a significant step toward the large-scale deployment of practical, high-performance, cost-effective, and highly secure quantum key distribution networks using standard telecommunication components.

quant-ph↗

arXiv2024

Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions

The postselection technique is an important proof technique for proving the security of quantum key distribution protocols against coherent attacks. In this work, we go through multiple steps to rigorously apply the postselection technique to optical quantum key distribution protocols. First, we place the postselection technique on a rigorous mathematical foundation by fixing a technical flaw in the original postselection paper. Second, we extend the applicability of the postselection technique to prepare-and-measure protocols by using a de Finetti reduction with a fixed marginal. Third, we show how the postselection technique can be used for decoy-state protocols by tagging the source. Finally, we extend the applicability of the postselection technique to realistic optical setups by developing a new variant of the flag-state squasher. We also improve existing de Finetti reductions, which reduce the effect of using the postselection technique on the key rate. These improvements can be more generally applied to other quantum information processing tasks. As an example to demonstrate the applicability of our work, we apply our results to the time-bin encoded three-state protocol. We observe that the postselection technique performs better than all other known proof techniques against coherent attacks.

quant-ph↗

arXiv2024

Composable free-space continuous-variable quantum key distribution using discrete modulation

Continuous-variable (CV) quantum key distribution (QKD) allows for quantum secure communication with the benefit of being close to existing classical coherent communication. In recent years, CV QKD protocols using a discrete number of displaced coherent states have been studied intensively, as the modulation can be directly implemented with real devices with a finite digital resolution. However, the experimental demonstrations until now only calculated key rates in the asymptotic regime. To be used in cryptographic applications, a QKD system has to generate keys with composable security in the finite-size regime. In this paper, we present a CV QKD system using discrete modulation that is especially designed for urban atmospheric channels. For this, we use polarization encoding to cope with the turbulent but non-birefringent atmosphere. This will allow to expand CV QKD networks beyond the existing fiber backbone. In a first laboratory demonstration, we implemented a novel type of security proof allowing to calculate composable finite-size key rates against i.i.d. collective attacks without any Gaussian assumptions. We applied the full QKD protocol including a QRNG, error correction and privacy amplification to extract secret keys. In particular, we studied the impact of frame errors on the actual key generation.

quant-ph↗

arXiv2024

Improved Decoy-state and Flag-state Squashing Methods

In this work, we present an improved analysis for decoy-state methods, enhancing both achievable key rates and recovering analytical results for the single intensity scenario. Our primary focus is improving the shortcomings observed in current decoy-state methods, particularly recovering results when employing no decoy intensities. Our methods enable the continuous interpolation across varying numbers of intensity settings. Additionally, we extend decoy-state techniques to encompass scenarios where intensities vary depending on the signal state, thereby relaxing the constraints on experimental implementations. Our findings demonstrate that a minimum of two intensities are sufficient for high asymptotic secret key rates, thereby further softening experimental requirements. Additionally, we address inherent imperfections within detection setups like imperfect beamsplitters. We derive provable secure lower bounds on the subspace population estimation, which is required for certain squashing methods such as the flag-state squasher. These analytical bounds allow us to encompass arbitrary passive linear optical setups, and together with intensities varying with each signal state, lets us include a broad class of experimental setups.

quant-ph↗

arXiv2024

Security Proof for Variable-Length Quantum Key Distribution

We present a security proof for variable-length QKD in the Renner framework against IID collective attacks. Our proof can be lifted to coherent attacks using the postselection technique. Our first main result is a theorem to convert a series of security proofs for fixed-length protocols satisfying certain conditions to a security proof for a variable-length protocol. This conversion requires no new calculations, does not require any changes to the final key lengths or the amount of error-correction information, and at most doubles the security parameter. Our second main result is the description and security proof of a more general class of variable-length QKD protocols, which does not require characterizing the honest behaviour of the channel connecting the users before the execution of the QKD protocol. Instead, these protocols adaptively determine the length of the final key, and the amount of information to be used for error-correction, based upon the observations made during the protocol. We apply these results to the qubit BB84 protocol, and show that variable-length implementations lead to higher expected key rates than the fixed-length implementations.

quant-ph↗