Phase Estimation of Coherent States with a Noiseless Linear Amplifier

TL;DR

This paper investigates the potential of noiseless linear amplifiers to improve phase estimation of coherent states, concluding that on average they do not enhance precision unless abstention strategies are employed.

Contribution

It provides a detailed analysis of the quantum Fisher information for phase estimation with noiseless linear amplifiers, highlighting their limitations in quantum metrology.

Findings

Noiseless linear amplification does not improve average phase estimation precision.

Abstention strategies can potentially reduce estimation cost.

The protocol's success probability impacts its effectiveness in metrology.

Abstract

Amplification of quantum states is inevitably accompanied with the introduction of noise at the output. For protocols that are probabilistic with heralded success, noiseless linear amplification in theory may still possible. When the protocol is successful, it can lead to an output that is a noiselessly amplified copy of the input. When the protocol is unsuccessful, the output state is degraded and is usually discarded. Probabilistic protocols may improve the performance of some quantum information protocols, but not for metrology if the whole statistics is taken into consideration. We calculate the precision limits on estimating the phase of coherent states using a noiseless linear amplifier by computing its quantum Fisher information and we show that on average, the noiseless linear amplifier does not improve the phase estimate. We also discuss the case where abstention from measurement can reduce the cost for estimation.