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arXiv:1707.04599 · Physical Review A

Finite-size analysis of measurement-device-independent quantum cryptography with continuous variables

Panagiotis Papanastasiou, Carlo Ottaviani, Stefano Pirandola

Published Oct 23, 2017• 79 citations
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Abstract

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 ${10}^{6}$ and ${10}^{9}$ data points may provide key rates $\ensuremath{\sim}{10}^{\ensuremath{-}2}$ bit/use over metropolitan distances.

DOI
10.1103/physreva.96.042332

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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∼10\ensuremath−2\ensuremath{\sim}{10}^{\ensuremath{-}2}\ensuremath∼10\ensuremath−2 bit/use over metropolitan distances.
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 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.
We have introduced, for the first time, a protocol for Continuous-Variable Measurement-Device-Independent Quantum Key Distribution (CV-MDI-QKD) in the terahertz (THz) frequency band. We have conducted a secret key rate analysis against collective attacks. The proposed THz CV-MDI-QKD is immune to all detector attacks, significantly enhancing the security assurance of practical THz CVQKD implementations. Furthermore, we investigated the impact of finite key length (the finite-size effect) and finite reconciliation efficiency on the performance of practical THz CV-MDI-QKD systems. Our findings reveal that by employing a large number of keys or signals and optimizing the modulation variance, the detrimental effects arising from the finite-size effect and suboptimal reconciliation efficiency can be notably mitigated. These insights play a crucial role in advancing the feasibility of THz CVQKD technology towards practical applications.
In this thesis we study the finite-size analysis of two continuous-variables quantum key distribution schemes. The first one is the one-way protocol using Gaussian modulation of thermal states and the other is the measurement-device-independent protocol. To do so, we adopt an efficient channel parameter estimation method based on the assumption of the Gaussian variables and the central limit theorem introduced by Ruppert et al. [Phys. Rev. A 90, 062310 (2014)]. Furthermore, we present a composable security analysis of the measurement device independent protocol for coherent attacks with a channel parameter estimation that is not based on the central limit theorem. We also investigated, in the asymptotic regime, an asymmetric situation for the authenticated parties against the eavesdropper caused by fast-fading channels. Here we assume that the eavesdropper has the full control of the communication channel and can instantaneously change its transmissivity in every use of it. We assumed the simple model of a uniform fading and addressed the cases of one-way protocols, continuous-measurement device-independent protocol in symmetric configuration and its star network extension for three users. Finally, we extended the asymptotic study of the one-way protocols using an arbitrary number of phase-encoded coherent states assuming a thermal loss channel without using a Gaussian approximation.
The measurement-device-independent quantum key distribution (MDI-QKD) protocol is immune to imperfect measurement devices. However, its practicality and performance when implemented in continuous-variable (CV) mode are still not satisfactory. We propose a CV-MDI-QKD protocol based on modulated squeezed states, and analyze its security against two-mode Gaussian attack. The results show that the protocol can achieve a higher secret key rate and transmission distance than previous coherent-state and squeezed-state protocols. A method to compensate the imperfection of a practical homodyne detector using phase-sensitive optical amplifiers is also presented. By setting an appropriate optical amplification gain, realistic detectors with ordinary quantum efficiency can be employed. In addition, we discuss the impact of finite-size effects on the secret key rate of the protocol. The methods presented may aid in the practical application of the CV-MDI-QKD protocol.
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.