A no-go theorem on the nature of the gravitational field beyond quantum theory

TL;DR

This paper uses a broad theoretical framework to show that gravity cannot be both classical and generate entanglement, challenging assumptions about the quantum nature of gravity based on entanglement experiments.

Contribution

It introduces a systematic GPT-based approach to analyze gravitational theories and proves a no-go theorem linking classicality, entanglement, and mediating role of gravity.

Findings

Gravity cannot be classical if it generates entanglement.

Gravity mediating interactions and being classical are incompatible.

Non-linear models like Schrödinger-Newton violate the theorem's conditions.

Abstract

Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled solely due to the gravitational interaction. Typically, this question has been addressed by assuming a specific physical theory to describe the gravitational interaction, but no systematic approach to characterise the set of possible gravitational theories which are compatible with the observation of entanglement has been proposed. Here, we remedy this by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework enables us to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two systems. We prove a no-go theorem stating that the following statements are incompatible: i) gravity is able to generate entanglement; ii) gravity mediates the interaction between the systems; iii) gravity is classical. We analyse the violation of each condition, in particular with respect to alternative non-linear models such as the Schr\"odinger-Newton equation and Collapse Models.