Unconditional Security of Coherent-State Quantum Key Distribution with a Strong Phase-Reference Pulse

We prove the unconditional security of a quantum key distribution protocol in which bit values are encoded in the phase of a weak coherent-state pulse relative to a strong reference pulse. In contrast with implementations in which a weak pulse is used as a substitute for a single-photon source, the achievable key rate is found to decrease only linearly with the transmission of the channel.

Figure 1

(a) A scheme with a strong reference pulse. (b) An equivalent scheme except that Eve’s region is extended.

Figure 2

Key gain $G$ is positive in the region between the two solid curves. $\eta =0.01$ and (a) $|\alpha {|}^2=0.5$, (b) $|\alpha {|}^2={10}^{-3}$.

Figure 3

Key gain $G$ versus transmission $\eta$. (a) $\zeta =\gamma =0$. (b) $\zeta =3\%$, $\gamma =0$. (c) BB84 with an ideal single-photon source for no errors. (d) BB84 with a coherent-state source for no errors. (a”)–(d”) The same except for inclusion of dark counting rate $\gamma ={10}^{-4}$.