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arXiv:1704.07924 · Physical Review A

Continuous-variable measurement-device-independent quantum key distribution: Composable security against coherent attacks

Cosmo Lupo, Carlo Ottaviani, Panagiotis Papanastasiou, Stefano Pirandola

Published May 29, 2018• 103 citations
arXivHTMLPDF

Abstract

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 ${10}^{7}$--${10}^{9}$ quantum signal transmissions, depending on loss and noise, and on the required level of security.

DOI
10.1103/physreva.97.052327

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We give the first composable security proof for continuous-variable quantum key distribution with coherent states against collective attacks. Crucially, in the limit of large blocks the secret key rate converges to the usual value computed from the Holevo bound. Combining our proof with either the de Finetti theorem or the postselection technique then shows the security of the protocol against general attacks, thereby confirming the long-standing conjecture that Gaussian attacks are optimal asymptotically in the composable security framework. We expect that our parameter estimation procedure, which does not rely on any assumption about the quantum state being measured, will find applications elsewhere, for instance, for the reliable quantification of continuous-variable entanglement in finite-size settings.
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.
Abstract A general security proof of continuous variable (CV) measurement device independent (MDI) quantum key distribution (QKD) should not be automatically reduced to the analysis of one-mode Gaussian attacks (in particular, independent entangling-cloner attacks). To stress this point, the present work provides a very simple (almost trivial) argument, showing that there are an infinite number of two-mode Gaussian attacks that cannot be reduced to or simulated by one-mode Gaussian attacks. This result further confirms that the security analysis of CV-MDI-QKD must generally involve a careful minimization over two-mode attacks as originally performed in (Pirandola et al, 2015 Nature Photon. 9, 397–402; arXiv: 1312.4104 (2013)).
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.