Improved DIQKD protocols with finite-size analysis

Ernest Y.-Z. Tan1, Pavel Sekatski2,3, Jean-Daniel Bancal4, René Schwonnek5, Renato Renner1, Nicolas Sangouard4, and Charles C.-W. Lim6,7

1Institute for Theoretical Physics, ETH Zürich, Switzerland
2Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland
3Department of Applied Physics, University of Geneva, Chemin de Pinchat 22, 1211 Geneva, Switzerland
4Université Paris-Saclay, CEA, CNRS, Institut de physique théorique, 91191, Gif-sur-Yvette, France
5Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Germany
6Department of Electrical & Computer Engineering, National University of Singapore, Singapore
7Centre for Quantum Technologies, National University of Singapore, Singapore

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Updated version: The authors have uploaded version v5 of this work to the arXiv which may contain updates or corrections not contained in the published version v4. The authors left the following comment on the arXiv:
Corrected error in Chernoff bound formula


The security of finite-length keys is essential for the implementation of device-independent quantum key distribution (DIQKD). Presently, there are several finite-size DIQKD security proofs, but they are mostly focused on standard DIQKD protocols and do not directly apply to the recent improved DIQKD protocols based on noisy preprocessing, random key measurements, and modified CHSH inequalities. Here, we provide a general finite-size security proof that can simultaneously encompass these approaches, using tighter finite-size bounds than previous analyses. In doing so, we develop a method to compute tight lower bounds on the asymptotic keyrate for any such DIQKD protocol with binary inputs and outputs. With this, we show that positive asymptotic keyrates are achievable up to depolarizing noise values of $9.33\%$, exceeding all previously known noise thresholds. We also develop a modification to random-key-measurement protocols, using a pre-shared seed followed by a "seed recovery" step, which yields substantially higher net key generation rates by essentially removing the sifting factor. Some of our results may also improve the keyrates of device-independent randomness expansion.

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