Hybrid Heralded Noiseless Amplification with Finite-Cutoff Quantum Scissors

A noiseless linear amplifier (NLA) can probabilistically amplify an optical state without the noise required by deterministic phase-insensitive amplification. We study a hybrid amplifier in which a finite-cutoff quantum-scissor NLA is placed between two single-mode squeezers. Analysis based on an ideal (infinite cutoff) NLA finds a gain enhancement from the squeezing. We explore the physics of this enhancement as the cutoff of the quantum scissors is increased. The low-cutoff sequence shows how this gain enhancement emerges from the truncated Fock space. Cutoff 3 is the lowest order at which the additional even- and odd-photon components can both contribute to gain enhancement, albeit with some skewing of the coefficients which reduces the fidelity. As the cutoff is increased the fidelity improves. However, unlike the ideal transformation, the finite-cutoff device depends on the phase of the coherent amplitude relative to the squeezing axes, with states aligned with the anti-squeezing requiring higher cutoffs to achieve high fidelity. We track behavior to high cutoffs and eventually see the performance predicted in the ideal theory emerge.