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Scientific Reports

Composable security of CV-MDI-QKD with secret key rate and data processing

Panagiotis Papanastasiou, Alexander G. Mountogiannakis, Stefano Pirandola

Published Jul 19, 2023• 22 citations
Publisher

Abstract

We provide a rigorous security proof of continuous-variable measurement-device-independent quantum key distribution which incorporates finite-size effects and composable terms. In order to use realistic and optimized parameters and be able to derive results close to experimental expectations, we run protocol simulations supported by a Python library, including all the protocol operations, from simulating the quantum communication till the extraction of the final key.

DOI
10.1038/s41598-023-37699-5

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quant-pharXiv:2609.16105•Sep 16, 2026•0 citations
We provide a rigorous security proof of continuous-variable measurement-device-independent quantum key distribution which incorporates finite-size effects and composable terms. In order to use realistic and optimized parameters and be able to derive results close to experimental expectations, we run protocol simulations supported by a Python library, including all the protocol operations, from simulating the quantum communication till the extraction of the final key.
We present a rigorous security analysis of continuous-variable measurement-device-independent quantum key distribution (CV MDI QKD) in a finite-size scenario. The security proof is obtained in two steps: by first assessing the security against collective Gaussian attacks, and then extending to the most general class of coherent attacks via the Gaussian de Finetti reduction. Our result combines recent state-of-the-art security proofs for CV QKD with findings about min-entropy calculus and parameter estimation. In doing so, we improve the finite-size estimate of the secret key rate. Our conclusions confirm that CV MDI protocols allow for high rates on the metropolitan scale, and may achieve a nonzero secret key rate against the most general class of coherent attacks after 107{10}^{7}107--109{10}^{9}109 quantum signal transmissions, depending on loss and noise, and on the required level of security.
Continuous-variable (CV) quantum key distribution (QKD) employs the quadratures of a bosonic mode to establish a secret key between two remote parties, and this is usually achieved via a Gaussian modulation of coherent states. The resulting secret key rate depends not only on the loss and noise in the communication channel, but also on a series of data processing steps that are needed for transforming shared correlations into a final string of secret bits. Here we consider a Gaussian-modulated coherent-state protocol with homodyne detection in the general setting of composable finite-size security. After simulating the process of quantum communication, the output classical data are postprocessed via procedures of parameter estimation, error correction, and privacy amplification. In particular, we analyze the high signal-to-noise regime, which requires the use of high-rate (nonbinary) low-density parity check codes. We implement all these steps in a python-based library that allows one to investigate and optimize the protocol parameters to be used in practical experimental implementations of short-range CV-QKD.
Continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD) is immune to all detector side channel attacks, however its security requires trusted sources. We investigate the effects of source intensity errors, the most crucial source error, on the security of CV-MDI-QKD protocol with Gaussian-modulated coherent states. We establish a general source intensity errors model and derive the secret key rate based on different assumptions on the abilities of legal parties Alice and Bob. To avoid the adverse effects of the sources' intensity errors on CV-MDI-QKD, we present different data-processing schemes. We also assess the security of the protocol against collective Gaussian attacks in the finite-size scenario with composable security. Taking source intensity errors into consideration, we achieve improved security compared to previous demonstrations. Our results will provide a useful reference for practical implementations of CV-MDI-QKD.
We study the impact of the finite-size effect on the continuous-variable measurement-device-independent quantum key distribution (CV-MDI QKD) protocol, mainly considering the finite-size effect on the parameter estimation procedure. The central-limit theorem and maximum likelihood estimation theorem are used to estimate the parameters. We also analyze the relationship between the number of exchanged signals and the optimal modulation variance in the protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI QKD protocol has the farthest transmission distance in the finite-size scenario. Finally, we discuss the impact of finite-size effects related to the practical detection in the CV-MDI QKD protocol. The overall results indicate that the finite-size effect has a great influence on the secret-key rate of the CV-MDI QKD protocol and should not be ignored.
We study the impact of finite-size effects on the key rate of continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD), considering two-mode Gaussian attacks. Inspired by the parameter estimation technique developed in by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)], we adapt it to study CV-MDI-QKD and, assuming realistic experimental conditions, we analyze the impact of finite-size effects on the key rate. We find that the performance of the protocol approaches the ideal one, increasing the block size, and, most importantly, that blocks between 106{10}^{6}106 and 109{10}^{9}109 data points may provide key rates $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ bit/use over metropolitan distances.
Discrete-Modulated (DM) Continuous-Variable (CV) Quantum Key Distribution (QKD) is an experimentally attractive approach to quantum cryptography, offering high key rates over metropolitan-scale distances while relying on state-of-the-art telecom infrastructure. However, a fundamental gap has remained between this experimental promise and rigorous security: for more than two decades, DM CV-QKD has lacked a complete composable finite-size security proof against coherent attacks. Existing works either restrict the adversary to collective attacks, impose additional finite-dimensional assumptions, apply only to specific modulation formats, or fail to recover the known asymptotic rates. Here, we resolve this longstanding problem by establishing the first complete composable finite-size security proof for DM CV-QKD protocols against coherent attacks, incorporating imperfect detectors and both fixed- and variable-length protocol variants. Our proof introduces two central results of broader interest: an infinite-dimensional marginal-constrained entropy accumulation theorem (iMEAT) and a rigorous dimension-reduction technique that makes the infinite-dimensional security bounds numerically tractable. The resulting key rates recover the known asymptotic rates and outperform established finite-size bounds based on collective attacks, while yielding positive key rates beyond 707070km for experimentally relevant block sizes and parameters. Thus, our work closes a longstanding gap and places an experimentally attractive class of CV-QKD protocols on a rigorous composable security footing and provides a pathway towards their practical deployment.