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

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.

arXiv comment14 pages, 18 figures

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• The influence of the Earth's curved spacetime on Gaussian quantum coherence
• Characterization of quantum and classical correlations in the Earth curved space-time
• Estimation of gravitational acceleration with quantum optical interferometers
• Weak measurement effect on optimal estimation with lower and upper bound on relativistic metrology
• Outperforming classical estimation of Post-Newtonian parameters of Earth's gravitational field using quantum metrology