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 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 Schrödinger-Newton equation and Collapse Models.

Quantum superposition of causal structures as a universal resource for local implementation of nonlocal quantum operations

“…In our case, this information is carried by the gravitational field due to the mass. It is important to note here that as the mass is in spatial superposition, the gravitational field it produces is also quantum in nature (the space-time is in a superposition of two different metrics) [44][45][46]. In other words, the quantum gravitational field acts as a quantum channel that carries quantum information from the locations of the mass to Alice's and Bob's locations.…”

The weak field limit of quantum matter back-reacting on classical spacetime

“…Early attempts to construct such a theory were based on the semi-classical Einstein's equations [11][12][13]. However, if one takes the semi-classical equations as fundamental, then it is well-known that they are not consistent, leading to violations of the standard principles of quantum theory and a breakdown of either operational no-signalling, the Born rule, or composition of quantum systems under the tensor product [14][15][16][17][18]. Moreover, even if one prefers to consider classical gravity only as an effective theory, the semi-classical equations result in pathological behaviour when quantum fluctuations are large [13,[19][20][21] or even for classical statistical mixtures since it fails to take into account the correlation between the quantum and the classical degrees of freedom [22,23].…”

Decoherence of cosmological perturbations from boundary terms and the non-classicality of gravity

“…The entanglement caused by the gravitational interaction implies a non-trivial fact that gravity, as a mediator between the system and environment, cannot be classical according to the Local Operations and Classical Communication (LOCC) [36] (see also [37] for a proof with the Generalized Probabilistic Theory). Utilizing this fact, there have been some proposals to probe the non-classicality of gravity in laboratory through the entanglement [38][39][40][41].…”