I. Introduction
Phase-Sensitive amplifiers (PSAs) are known to provide linear amplification with noise figures (NFs) below the 3-dB quantum noise limit imposed on their phase-insensitive amplifier (PIA) counterparts [1]. Long interaction lengths in fiber devices enable us to access the gain regime in which all-optical phase regeneration of phase-encoded signals [2]–[4] can be performed. By utilizing a fiber-optical parametric amplifier (FOPA)-based PIA in saturation, amplitude regeneration of differential phase-shift-keying (DPSK) signals has also been demonstrated [5], [6], and saturated PIAs have also been proposed to reduce accumulated nonlinear phase jitter in transmission links [7].