In continuous-variables quantum key distribution with coherent states, the advantage of performing the detection by using standard telecoms components is counterbalanced by the lack of a stable phase reference in homodyne detection due to the complexity of optical phase-locking circuits and to the unavoidable phase noise of lasers, which introduces a degradation on the achievable secure key rate. Pilot-assisted phase-noise estimation and postdetection compensation techniques are used to implement a protocol with coherent states where a local laser is employed and it is not locked to the received signal, but a postdetection phase correction is applied. Here the reduction of the secure key rate determined by the laser phase noise, for both individual and collective attacks, is analytically evaluated and a scheme of pilot-assisted phase estimation proposed, outlining the tradeoff in the system design between phase noise and spectral efficiency. The optimal modulation variance as a function of the phase-noise amount is derived.

• Received 16 May 2016
• Revised 1 December 2016

DOI:https://doi.org/10.1103/PhysRevA.95.022315