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We consider discrete-alphabet encoding schemes for coherent-state quantum keydistribution. The sender encodes the letters of a finite-size alphabet intocoherent states whose amplitudes are symmetrically distributed on a circlecentered in the origin of the phase space. We study the asymptotic performanceof this phase-encoded coherent-state protocol in direct and reversereconciliation assuming both loss and thermal noise in the communicationchannel. In particular, we show that using just four phase-shifted coherentstates is sufficient for generating secret key rates of the order of $4 \times10^{-3}$ bits per channel use at about 15 dB loss in the presence of realisticexcess noise.

Quantum key distribution with phase-encoded coherent states: Asymptotic security analysis in thermal-loss channels