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 multispan link employing either phase-insensitive or phase-sensitive 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 composable 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 for both kinds of amplified links with the no-amplifier protocol, identifying the enhancement introduced by optical amplification.