Estimating space-time parameters with a quantum probe in a lossy environment

TL;DR

This paper investigates how to accurately estimate the Schwarzschild radius using Gaussian quantum probes in lossy environments, highlighting the advantages of squeezed states and optimized frequency profiles for improved precision.

Contribution

It introduces a practical method to compute Quantum Fisher Information for lossy channels and identifies optimal conditions and wavepacket profiles for enhanced estimation accuracy.

Findings

Squeezed states can outperform coherent states under certain loss conditions.

Optimized frequency profiles, especially smooth rectangular ones, improve estimation precision.

A new approach to calculate QFI in lossy quantum communication scenarios.

Abstract

We study the problem of estimating the Schwarzschild radius of a massive body using Gaussian quantum probe states. Previous calculations assumed that the probe state remained pure after propagating a large distance. In a realistic scenario, there would be inevitable losses. Here we introduce a practical approach to calculate the Quantum Fisher Informations (QFIs) for a quantum probe that has passed through a lossy channel. Whilst for many situations loss means coherent states are optimal, we identify certain situations for which squeezed states have an advantage. We also study the effect of the frequency profile of the wavepacket propagating from Alice to Bob. There exists an optimal operating point for a chosen mode profile. In particular, employing a smooth rectangular frequency profile significantly improves the error bound on the Schwarzschild radius compared to a Gaussian frequency profile.