Models of reduced-noise, probabilistic linear amplifiers

We construct an amplifier that interpolates between a nondeterministic, immaculate linear amplifier and a deterministic, ideal linear amplifier and beyond to nonideal linear amplifiers. The construction involves cascading an immaculate linear amplifier that has amplitude gain $g_1$ with a (possibly) nonideal linear amplifier that has gain $g_2$. With respect to normally ordered moments, the device has output noise ${\mu }^2(G^2-1)$ where $G=g_1{g}_2$ is the overall amplitude gain and ${\mu }^2$ is a noise parameter. When ${\mu }^2\ge 1$, our devices realize ideal (${\mu }^2=1$) and nonideal (${\mu }^2>1$) linear amplifiers. When $0\le {\mu }^2<1$, these devices work effectively only over a restricted region of phase space and with some subunity success probability $p_{\mathrm{✓}}$. We investigate the performance of our ${\mu }^2$-amplifiers in terms of a gain-corrected probability-fidelity product and the ratio of input to output signal-to-noise ratios corrected for success probability.