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arXiv:1003.5766 · Journal of Physics A Mathematical and Theoretical

Secure key rate of the BB84 protocol using finite sample bits

Yousuke Sano, Ryutaroh Matsumoto, Tomohiko Uyematsu

Published Nov 15, 2010• 19 citations
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Abstract

We improve the non-asymptotic key rate shown by Scarani and Renner by proposing several methods to construct tighter conservative confidence intervals of the phase error rate than one previously shown.In addition, we show that the accurate channel estimation method non-asymptotically increases the key rate over the amplitude damping channel as well as the asymptotic case in the BB84 protocol.

DOI
10.1088/1751-8113/43/49/495302

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We improve the non-asymptotic key rate shown by Scarani and Renner by proposing several methods to construct tighter conservative confidence intervals of the phase error rate than one previously shown.In addition, we show that the accurate channel estimation method non-asymptotically increases the key rate over the amplitude damping channel as well as the asymptotic case in the BB84 protocol.
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on the IBM quantum processors, that B92 is the optimal protocol under amplitude-damping and generalized amplitude-damping noise. We then show that the security of the noisy BBM92 protocol crucially depends on the type and the mode of distribution of an entangled pair. Finally, we implement an error-corrected BB84 protocol using dual-rail encoding on a noisy quantum processor, and show that the dual-rail BB84 implementation outperforms the conventional BB84 in the presence of noise. Our secure key rate calculation also takes into account the effects of CNOT imperfections on the error rates of the protocols.
In this paper we consider a three-state variant of the BB84 quantum key distribution (QKD) protocol. We derive a new lower-bound on the key rate of this protocol in the asymptotic scenario and use mismatched measurement outcomes to improve the channel estimation. Our new key rate bound remains positive up to an error rate of 11%11\%11%, exactly that achieved by the four-state BB84 protocol.