Can quantum probes satisfy the weak equivalence principle?

TL;DR

This paper investigates whether quantum probes in gravitational fields obey the weak equivalence principle by proposing a quantum-compatible formulation and analyzing the effects of gravity gradients on measurement information.

Contribution

It introduces a formulation of the WEP applicable to quantum regimes and demonstrates how gravity gradients can violate this principle for quantum probes.

Findings

Quantum probes satisfy the WEP in uniform gravitational fields.

Gravity gradients can encode mass information, violating the WEP.

The formulation links Fisher information to the WEP in quantum measurements.

Abstract

We address the question whether quantum probes in a gravitational field can be considered as test particles obeying the weak equivalence principle (WEP). A formulation of the WEP is proposed which applies also in the quantum regime, while maintaining the physical content of its classical counterpart. Such formulation requires the introduction of a gravitational field not to modify the Fisher information about the mass of a freely-falling probe, extractable through measurements of its position. We discover that, while in a uniform field quantum probes satisfy our formulation of the WEP exactly, gravity gradients can encode nontrivial information about the particle's mass in its wavefunction, leading to violations of the WEP.