Continuous-variable quantum key distribution over multispan links employing phase-insensitive and phase-sensitive amplifiers

Transmission losses through optical fibers are one of the main obstacles preventing both long-distance quantum communications and continuous-variable quantum key distribution. Optical amplification provides a tool to obtain, at least partially, signal restoration. In this work, we address a key distribution protocol over a multi-span link employing either phase-insensitive (PIA) or phase-sensitive (PSA) amplifiers, considering Gaussian modulation of coherent states followed by homodyne detection at the receiver's side. We perform the security analysis under both unconditional and conditional security frameworks by assuming in the latter case only a single span of the whole communication link to be untrusted. We compare the resulting key generation rate (KGR) for both kinds of amplified links with the no-amplifier protocol, identifying the enhancement introduced by optical amplification. We prove an increase in the KGR for the PSA link in the unconditional scenario and for both PSA and PIA in the conditional security setting depending on position of the attack and the measured quadrature.