arXiv subjects

Amir Arqand

Publications and source records attributed to Amir Arqand.

8 recordsLinked to original sources

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.

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arXiv2025

Generalized Rényi entropy accumulation theorem and generalized quantum probability estimation

The entropy accumulation theorem, and its subsequent generalized version, is a powerful tool in the security analysis of many device-dependent and device-independent cryptography protocols. However, it has the drawback that the finite-size bounds it yields are not necessarily optimal, and furthermore it relies on the construction of an affine min-tradeoff function, which can often be challenging to construct optimally in practice. In this work, we address both of these challenges simultaneously by deriving a new entropy accumulation bound. Our bound yields significantly better finite-size performance, and can be computed as an intuitively interpretable convex optimization, without any specification of affine min-tradeoff functions. Furthermore, it can be applied directly at the level of Rényi entropies if desired, yielding fully-Rényi security proofs. Our proof techniques are based on elaborating on a connection between entropy accumulation and the frameworks of quantum probability estimation or $f$-weighted Rényi entropies, and in the process we obtain some new results with respect to those frameworks as well. In particular, those findings imply that our bounds apply to prepare-and-measure protocols without the virtual tomography procedures or repetition-rate restrictions previously required for entropy accumulation.

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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.

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arXiv2025

Marginal-constrained entropy accumulation theorem

We derive a novel chain rule for a family of channel conditional entropies, covering von Neumann and sandwiched Rényi entropies. In the process, we show that these channel conditional entropies are equal to their regularized version, and more generally, additive across tensor products of channels. For the purposes of cryptography, applying our chain rule to sequences of channels yields a new variant of Rényi entropy accumulation, in which we can impose some specific forms of marginal-state constraint on the input states to each individual channel. This generalizes a recently introduced security proof technique that was developed to analyze prepare-and-measure QKD with no limitations on the repetition rate. In particular, our generalization yields ``fully adaptive'' protocols that can in principle update the entropy estimation procedure during the protocol itself, similar to the quantum probability estimation framework.

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arXiv2024

Mutual information chain rules for security proofs robust against device imperfections

In this work we derive a number of chain rules for mutual information quantities, suitable for analyzing quantum cryptography with imperfect devices that leak additional information to an adversary. First, we derive a chain rule between smooth min-entropy and smooth max-information, which improves over previous chain rules for characterizing one-shot information leakage caused by an additional conditioning register. Second, we derive an ''information bounding theorem'' that bounds the Rényi mutual information of a state produced by a sequence of channels, in terms of the Rényi mutual information of the individual channel outputs, similar to entropy accumulation theorems. In particular, this yields simple bounds on the smooth max-information in the preceding chain rule. Third, we derive chain rules between Rényi entropies and Rényi mutual information, which can be used to modify the entropy accumulation theorem to accommodate leakage registers sent to the adversary in each round of a protocol. We show that these results can be used to handle some device imperfections in a variety of device-dependent and device-independent protocols, such as randomness generation and quantum key distribution.

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arXiv2023

Lipschitz continuity of quantum-classical conditional entropies with respect to angular distance and related properties

We derive a Lipschitz continuity bound for quantum-classical conditional entropies with respect to angular distance, with a Lipschitz constant that is independent of the dimension of the conditioning system. This bound is sharper in some situations than previous continuity bounds, which were either based on trace distance (where Lipschitz continuity is not possible), or based on angular distance but did not include a conditioning system. However, we find that the bound does not directly generalize to fully quantum conditional entropies. To investigate possible counterexamples in that setting, we study the characterization of states which saturate the Fuchs--van de Graaf inequality and thus have angular distance approximately equal to trace distance. We give an exact characterization of such states in the invertible case. For the noninvertible case, we show that the situation appears to be significantly more elaborate, and seems to be strongly connected to the question of characterizing the set of fidelity-preserving measurements.

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arXiv2022

Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel

We study the LOCC-assisted quantum capacity of bosonic dephasing channel with energy constraint on input states. We start our analysis by focusing on the energy-constrained squashed entanglement of the channel, which is an upper bound for the energy-constrained LOCC-assisted quantum capacity. As computing energy-constrained squashed entanglement of the channel is challenging due to a double optimization (over the set of density matrices and the isometric extensions of a squashing channel), we first derive an upper bound for it, and then we discuss how tight that bound is for energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel. We prove that the optimal input state is diagonal in the Fock basis. Furthermore, we prove that for a generic channel, the optimal squashing channel belongs to the set of symmetric quantum Markov chain inducer (SQMCI) channels of the channel system-environment output, provided that such a set is non-empty. With supporting arguments, we conjecture that this is instead the case for the bosonic dephasing channel. Hence, for it we analyze two explicit examples of squashing channels which are not SQMCI, but are symmetric. Through them, we derive explicit upper and lower bounds for the energy-constrained LOCC-assisted quantum capacity of the bosonic dephasing channel in terms of its quantum capacity with different noise parameters. As the difference between upper and lower bounds is at most of the order $10^{-1}$, we conclude that the bounds are tight. Hence we provide a very good estimation of the LOCC-assisted quantum capacity of the bosonic dephasing channel.

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arXiv2021

Quantum capacity of bosonic dephasing channel

We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing rates.

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