Security of coherent-state key distribution through an amplifying channel

Security of coherent-state quantum key distribution with homodyne or heterodyne detection through phase-insensitive amplifying channel is analyzed. Contrary to a lossy channel, the security against collective attacks is guaranteed for any ideal amplification in the channel if the direct reconciliation is applied. If there is excess noise during amplification, the threshold on the security against the collective attacks is determined. Opposite to the lossy channel, the most robust setup against the excess noise is a coherent-state key distribution with homodyne detection and direct reconciliation.