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

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 due to solely the gravitational interaction. Typically, this question has been addressed by assuming an underlying 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 introduce the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field. This framework has the advantage that it only relies on the set of operationally accessible states, transformations, and measurements, without presupposing an underlying theory. Hence, it provides a framework to systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two non-classical systems. Assuming that such entanglement is observed we prove a no-go theorem stating that the following statements are incompatible: i) the two non-classical systems are independent subsystems, ii) the gravitational field is a physical degree of freedom which mediates the interaction and iii) the gravitational field is classical. Moreover we argue that conditions i) and ii) should be met, and hence that the gravitational field is non-classical. Non-classicality does not imply that the gravitational field is quantum, and to illustrate this we provide examples of non-classical and non-quantum theories which are logically consistent with the other conditions.Comment: 12 pages main text; 23 pages Appendices; many diagrams. Improved presentation compared to the first versio