Quantum limits on probabilistic amplifiers

TL;DR

This paper establishes fundamental quantum limits on the success probabilities of probabilistic and approximate immaculate amplifiers, revealing that phase-insensitive devices have very low success rates, while phase-sensitive ones can perform better.

Contribution

It provides theoretical bounds on the working probabilities of probabilistic quantum amplifiers and constructs models achieving some of these bounds.

Findings

Phase-insensitive immaculate amplifiers have very low success probabilities.

Phase-sensitive immaculate amplifiers can have higher success probabilities when targeting specific coherent states.

Theoretical models demonstrate the feasibility of approaching these probability bounds.

Abstract

An ideal phase-preserving linear amplifier is a deterministic device that adds to an input signal the minimal amount of noise consistent with the constraints imposed by quantum mechanics. A noiseless linear amplifier takes an input coherent state to an amplified coherent state, but only works part of the time. Such a device is actually better than noiseless, since the output has less noise than the amplified noise of the input coherent state; for this reason we refer to such devices as {\em immaculate}. Here we bound the working probabilities of probabilistic and approximate immaculate amplifiers and construct theoretical models that achieve some of these bounds. Our chief conclusions are the following: (i) the working probability of any phase-insensitive immaculate amplifier is very small in the phase-plane region where the device works with high fidelity; (ii) phase-sensitive immaculate amplifiers that work only on coherent states sparsely distributed on a phase-plane circle centered at the origin can have a reasonably high working probability.