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Due to the pervasive nature of decoherence, protection of quantum informationduring transmission is of critical importance for any quantum network. A linearamplifier that can enhance quantum signals stronger than their associated noisewhile preserving quantum coherence is therefore of great use. This seeminglyunphysical amplifier property is achievable for a class of probabilisticamplifiers that does not work deterministically. Here we present a linearamplification scheme that realises this property for coherent states bycombining a heralded measurement-based noiseless linear amplifier and adeterministic linear amplifier. The concatenation of two amplifiers introducesthe flexibility that allows one to tune between the regimes of high-gain orhigh noise-reduction, and control the trade-off of these performances against afinite heralding probability. We demonstrate an amplification signal transfercoefficient of $\mathcal{T}_s > 1$ with no statistical distortion of the outputstate. By partially relaxing the demand of output Gaussianity, we can obtainfurther improvement to achieve a $\mathcal{T}_s = 2.55 \pm 0.08$. Ouramplification scheme only relies on linear optics and post-selection algorithm.We discuss the potential of using this amplifier as a building block inextending the distance of quantum communication.

Quantum enhancement of signal-to-noise ratio with a heralded linear amplifier