Efficient noiseless linear amplification for light fields with larger amplitudes

We suggest and investigate a scheme for non-deterministic noiseless linear amplification of coherent states using successive photon addition, (â†)², where ↠is the photon creation operator. We compare it with a previous proposal using the photon addition-then-subtraction, ââ†, where â is the photon annihilation operator, that works as an appropriate amplifier only for weak light fields. We show that when the amplitude of a coherent state is |α| >∼ 0.91, the (â†)² operation serves as a more efficient amplifier compared to the â↠operation in terms of equivalent input noise. Using â↠and (â†)² as basic building blocks, we compare combinatorial amplifications of coherent states using (ââ†)², â†⁴, â↠↲, and ↲ââ†, and show that (ââ†)², ↲ââ†, and â†⁴ exhibit strongest noiseless properties for |α| >∼ 0.51, 0.51 <∼ |α| <∼ 1.05, and |α| >∼ 1.05, respectively. We further show that the (â†)² operation can be useful for amplifying superpositions of the coherent states. In contrast to previous studies, our work provides efficient schemes to implement a noiseless amplifier for light fields with medium and large amplitudes.