Shlok Ashok Nahar

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.

Security proofs for quantum key distribution (QKD) based on the entropic uncertainty relations and the phase-error approach have the advantage of producing some of the tightest key rates against coherent attacks. We prove the security of QKD using the entropic uncertainty relations, for scenarios where Eve is allowed full control of the detection efficiency and dark rates of all detectors within some specified ranges. Thus, our work solves the practically important problem of detector side channels. Our work also removes the requirement of ``basis-independent loss'' required by these proof techniques. Thus, we render these proof techniques applicable to practical QKD scenarios. Furthermore, we prove security for variable-length QKD protocols, which do not require Alice and Bob to characterize the honest behaviour of the channel.

Proving the security of quantum key distribution (QKD) protocols against arbitrary attacks is a challenging task for arbitrary protocols. Here, we accomplish this task by extending and improving both the decoy-state analysis against collective attacks, and the postselection technique to uplift this security proof to arbitrary attacks. First, we improve the postselection technique - both by improving the cost paid for the uplift, and by rigorously showing how it can be applied to generic optical protocols. Second, we fundamentally improve the decoy-state analysis in such a way that we require only one decoy intensity to achieve the same performance as prior analysis with two decoy intensities. This has two consequences - it makes the protocol easier to practically implement, and reduces the penalty incurred by using the postselection technique. Third, we extend the finite-size QKD analysis to decoy-state protocols and generically improve the finite-size correction terms that appear. Thus, we provide a full security proof against arbitrary attacks for generic decoy-state protocols.

Quantum Key Distribution (QKD) protocols rely on authenticated classical communication. Typical QKD security proofs are carried out in an idealized setting where authentication is assumed to behave honestly: it never aborts, and all classical messages are delivered faithfully with their original timing preserved. Authenticated channels that can be constructed in practice have different properties. Most critically, such channels may abort asymmetrically, such that only the receiving party may detect an authentication failure while the sending party remains unaware. Furthermore, an adversary may delay, reorder, or block classical messages. This discrepancy renders the standard QKD security definition and existing QKD security proofs invalid in the practical authentication setting. In this work we resolve this issue. Our main result is a reduction theorem showing that, under mild and easily satisfied protocol conditions, any QKD protocol proven secure under the honest authentication setting remains secure under a practical authentication setting. This result allows all existing QKD proofs to be retroactively lifted to the practical authentication setting with a minor protocol tweak.

Quantum Key Distribution (QKD) protocols rely on authenticated classical communication. Typical QKD security proofs are carried out in an idealized setting where authentication is assumed to behave honestly: it never aborts, and all classical messages are delivered faithfully with their original timing preserved. Authenticated channels that can be constructed in practice have different properties. Most critically, such channels may abort asymmetrically, such that only the receiving party may detect an authentication failure while the sending party remains unaware. Furthermore, an adversary may delay, reorder, or block classical messages. This discrepancy renders the standard QKD security definition and existing QKD security proofs invalid in the practical authentication setting. In this work we resolve this issue. Our main result is a reduction theorem showing that, under mild and easily satisfied protocol conditions, any QKD protocol proven secure under the honest authentication setting remains secure under a practical authentication setting. This result allows all existing QKD proofs to be retroactively lifted to the practical authentication setting with a minor protocol tweak.

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.

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 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, 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.

Quantum key distribution (QKD) promises information-theoretic security based on quantum mechanics, but practical implementations face security vulnerabilities due to device imperfections. While recent advances have separately addressed source and detector imperfections, real-world QKD systems suffer from both simultaneously. Here, we demonstrate that existing phase-error-estimation-based security proof techniques can be integrated into a unified security proof that simultaneously accounts for both types of imperfections. This represents an important step toward closing the gap between theoretical security proofs and practical QKD implementations.

We provide a security proof for quantum key distribution (QKD) protocols using passive detection setups within the entropic uncertainty relation (EUR) framework. Passive detection avoids the need for active basis choice but introduces challenges due to beam splitters and imperfections in detectors. We show how to define and bound the phase-error rate in passive detection setups, even when detector imperfections are not precisely known but lie within known ranges. Our analysis applies in the finite-size regime against general coherent attacks.

We discuss the status of security proofs for practical decoy-state Quantum Key Distribution using the BB84 protocol, pertaining to optical implementations using weak coherent pulses and threshold photo-detectors. Our focus is on the gaps in the existing literature. Gaps might result, for example, from a mismatch of protocol detail choices and proof technique elements, from proofs relying on earlier results that made different assumptions, or from protocol choices that do not consider real-world requirements. While substantial progress has been made, our overview draws attention to the details that still require our attention.

The postselection technique is a widely used tool to lift the security of Quantum Key Distribution (QKD) protocols against IID collective attacks to coherent attacks. While various other approaches for proving security against coherent attacks exist, they have limitations that make them less suitable for typical optical prepare-and-measure protocols. We identify and address some limitations of the postselection technique as applied to optical prepare-and-measure QKD protocols. We extend this analysis to decoy-state protocols, which are essential for long-distance QKD. Finally, we also improve the practical applicability of the postselection technique. Thus, we argue that the postselection technique, with the relevant modifications, is the only lift to coherent attacks that can be broadly applied to optical implementations of generic prepare-and-measure QKD protocols.

Quantum dot-based entangled photon sources are promising candidates for quantum key distribution (QKD), as they can in principle emit deterministically, with high brightness and low multiphoton contribution. However, quantum dots (QD) often inherently possess a fine structure splitting (FSS). Since the entangled photonic state in the presence of non-zero FSS is oscillating, one must settle for a lower efficiency source through temporal post-selection or a lower measured entanglement fidelity. In both cases, the overall key rate is reduced. Our QKD analysis shows that this trade-off can be overcome by constructing a time-resolved QKD protocol where all photon pairs emitted by a QD with non-zero FSS can be used in secret key generation. This protocol works only when the detection system's temporal resolution is much smaller than the FSS period. By implementing our protocol, higher key rates can be achieved as compared to previous QKD experiments with QD entangled photon pair sources. Additionally, unlike previous security analyses that assume perfect qubit states, we rigorously bound the effect of any multi-photon components of the optical state on the key rate, which is more applicable to practical implementations.

The coherent one-way (COW) protocol is a promising commercial solution to practical quantum key distribution (QKD) due to its simple optical implementation. However, the non-IID structure of COW due to its inter-signal coherence makes standard security analysis inapplicable. Recently, it has been shown that a modified COW setup allows standard IID analysis, but at the cost of imposing extra limitations and increasing the number of pulses required for each bit. Here we propose a variant that possesses the IID structure and completely retains the optical setup of COW, but with a different data processing scheme that ignores inter-signal information. We obtain key rate lower bound close to analysis for the previously proposed IID variant, and achieves a higher number of key bits transmitted per second.

We develop general tools to be able to numerically calculate key rates for quantum key distribution protocols with characterized source defects. These tools include performing decoy-state analysis for optical protocols where the signal states are not fully phase-randomised. We apply these tools for the three-state protocol when the signal states are not fully phase-randomised due to a high repetition rate. Our results suggest that the small amounts of residual coherences do not greatly affect the key rate.

In this work, we present an open-source software platform that calculates key rate for general QKD protocols, building upon the numerical framework proposed by our group that can perform automated security proof of QKD protocols. The software platform is fully modularized with mutually independent modules for descriptions of protocols/channels, solvers for bounding key rate, and parameter optimization algorithms. It currently supports BB84 and measurement-device-independent QKD (including decoy states), as well as discrete-modulated continuous variable QKD. It also supports finite-size analysis for non-decoy-state protocols. We hope that the open-sourcing can attract theorists to test new protocols and/or contribute to new solvers, as well as appeal to experimentalists who wish to analyze their data or optimize parameters for new experiments.

A numerical approach for the calculation of QKD key rates allows a uniform framework to be applied to general QKD protocols. Based on our group's previous work, we would like to build a universal software platform that is fully modularized and user-friendly, where one can easily swap in and out different QKD protocol descriptions, channel simulation models or experimental data, backend numerical solvers, and parameter optimization algorithms. Our goal is to build an open-source platform that can be both useful for theorists testing new protocols as well as experimentalists looking for optimal parameters or analyzing their experimental data.