Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution

TL;DR

This paper derives an exact expression for quantum Fisher information of entangled coherent states under photon losses, revealing a transition from quantum to classical phase sensitivity scaling due to decoherence.

Contribution

It provides an exact analytical solution for quantum Fisher information considering photon losses, highlighting the quantum-classical transition in phase sensitivity.

Findings

Sensitivity transitions from Heisenberg to classical scaling due to photon losses.

Quantum decoherence depends on the number of photons lost, not just the loss rate.

Crossover in sensitivity between entangled coherent and NOON states can occur at low photon loss.

Abstract

We investigate the performance of entangled coherent state for quantum enhanced phase estimation. An exact analytical expression of quantum Fisher information is derived to show the role of photon losses on the ultimate phase sensitivity. We find a transition of the sensitivity from the Heisenberg scaling to the classical scaling due to quantum decoherence of the photon state. This quantum-classical transition is uniquely determined by the number of photons being lost, instead of the number of incident photons or the photon loss rate alone. Our results also reveal that a crossover of the sensitivity between the entangled coherent state and the NOON state can occur even for very small photon loss rate.