Quantum-key-distribution protocols without sifting that are resistant to photon-number-splitting attacks

Abstract

We propose a family of sifting-less quantum-key-distribution protocols which use reverse reconciliation, and are based on weak coherent pulses (WCPs) polarized along $m$ different directions. When $m=4$, the physical part of the protocol is identical to most experimental implementations of BB84 [Bennett and Brassard, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (IEEE, New York, 1984)] and SARG04 [Scarani, Ac\'{\i}n, Ribordy, and Gisin, Phys. Rev. Lett. 92, 057901 (2004); Ac\'{\i}n, Gisin, and Scarani, Phys. Rev. A 69, 012309 (2004)] protocols and they differ only in classical communications and data processing. We compute their total key rate as a function of the channel transmission $T$, using general information theoretical arguments, and we show that they have a higher key rate than the more standard protocols, both for fixed and optimized average photon number of the WCPs. When no decoy-state protocols (DSPs) [Hwang, Phys. Rev. Lett. 91, 057901 (2003); Lo, Ma, and Chen, Phys. Rev. Lett. 94, 230504 (2005); Wang, Phys. Rev. A 72, 012322 (2005)] are applied, the scaling of the key rate with transmission is improved from ${T}^{2}$ for BB84 to ${T}^{1+\frac{1}{m\ensuremath{-}2}}$. If a DSP is applied, we show how the key rates scale linearly with $T$, with an improvement of the prefactor by 75.96% for $m=4$. High values of $m$ allow one to asymptotically approach the key rate obtained with ideal single-photon pulses. The fact that the key rates of these sifting-less protocols are higher compared to those of the aforementioned more standard protocols show that the latter are not optimal, since they do not extract all the available secret keys from the experimental correlations.