  When gravity is sourced by a quantum system, there is tension between its
role as the mediator of a fundamental interaction, which is expected to acquire
nonclassical features, and its role in determining the properties of spacetime,
which is inherently classical. Fundamentally, this tension should result in
breaking one of the fundamental principles of quantum theory or general
relativity, but it is usually hard to assess which one without resorting to a
specific model. Here, we answer this question in a theory-independent way using
General Probabilistic Theories (GPTs). We consider the interactions of the
gravitational field with a single matter system, and derive a no-go theorem
showing that when gravity is classical at least one of the following
assumptions needs to be violated: (i) Matter degrees of freedom are described
by fully non-classical degrees of freedom; (ii) Interactions between matter
degrees of freedom and the gravitational field are reversible; (iii) Matter
degrees of freedom back-react on the gravitational field. We argue that this
implies that theories of classical gravity and quantum matter must be
fundamentally irreversible, as is the case in the recent model of Oppenheim et
al. Conversely if we require that the interaction between quantum matter and
the gravitational field is reversible, then the gravitational field must be
non-classical.
