  We consider the noisy thermal amplifier channel, where signal modes are
amplified together with environmental thermal modes. We focus on the secret-key
capacity of this channel, which is the maximum amount of secret bits that two
remote parties can generate by means of the most general adaptive protocol,
assisted by unlimited and two-way classical communication. For this channel
only upper and lower bounds are known, and in this work we improve the lower
bound. We consider a protocol based on squeezed states and homodyne detections,
in both direct and reverse reconciliation. In particular, we assume that
trusted thermal noise is mixed on beam splitters controlled by the parties in a
way to assist their homodyne detections. The new improved lower bounds to the
secret-key capacity are obtained by optimizing the key rates over the variance
of the trusted noise injected, and the transmissivity of the parties' beam
splitters. Our results confirm that there is a separation between the coherent
information of the thermal amplifier channel and its secret key capacity.

Quantum Physics