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

TL;DR

This paper analyzes the security of a phase-encoded coherent-state quantum key distribution protocol in thermal-loss channels, demonstrating that four states can generate secure keys under realistic noise and loss conditions.

Contribution

It provides an asymptotic security analysis for a discrete-alphabet phase-encoded QKD scheme considering thermal noise and loss, highlighting the sufficiency of four states for practical key rates.

Findings

Four phase-shifted coherent states enable secure key generation at 15 dB loss.

Achieves key rates of approximately 4 x 10^{-3} bits per channel use.

Security holds under realistic excess noise conditions.

Abstract

We consider discrete-alphabet encoding schemes for coherent-state quantum key distribution. The sender encodes the letters of a finite-size alphabet into coherent states whose amplitudes are symmetrically distributed on a circle centered in the origin of the phase space. We study the asymptotic performance of this phase-encoded coherent-state protocol in direct and reverse reconciliation assuming both loss and thermal noise in the communication channel. In particular, we show that using just four phase-shifted coherent states is sufficient for generating secret key rates of the order of $4 \times 10^{-3}$ bits per channel use at about 15 dB loss in the presence of realistic excess noise.