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

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). Inspired by the parameter estimation technique developed in [Rupert \textit{et al.} Phys. Rev. A \textbf{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, increasing the block-size, the performance of the protocol converges towards the ideal one, and that block-sizes between $10^6$ and $10^9$ data points can already provide a key rate $\sim 10^{-2}$ bit/use over metropolitan distances.

10 pages, 3 figures, typos corrected, abstract and intro modified, references added

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