Abstract In this study, we analyse the efficiency of a protocol with discrete modulation of continuous variable non-Gaussian states, that is, the coherent states having the addition of one photon followed by the subtraction of one photon (PASCS). We calculate lower bounds of the asymptotic key rates against Gaussian collective attacks based on the fact that for sufficiently small modulation variances we remain close to the protocol with Gaussian modulation. We compare the results of a four-state protocol (quadrature phase-shift-keying) using PASCS with the ones using coherent states, and show that under the same environmental conditions, the former always outperforms the latter, allowing to increase the maximum possible distance for secret key generation. Interestingly, we find that for the protocol using discrete-modulated PASCS, the noisier the line, the better will be its performance compared to the protocol using coherent states, showing that continuous variable non-Gaussian states can be considerably more advantageous for performing quantum key distribution in non-ideal situations.
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