Abstract
Whether gravity must be quantized remains one of the biggest open problems in fundamental physics. Classical-quantum hybrid theories have recently attracted attention as a possible framework in which gravity is treated classically yet interacts consistently with quantum matter. Schemes based on completely positive dynamics satisfy most formal consistency requirements and enable a systematic treatment of quantum backreaction, but they also invite the question of whether the hybrid description is fundamental or instead an effective sector of a larger quantum theory. Here, we demonstrate that classical-quantum gravity based on completely positive dynamics admits an embedding into a fully quantum theory on an enlarged Hilbert space. As a complementary illustration, we consider a qubit interacting with a classical particle and demonstrate that the corresponding hybrid system violates angular momentum conservation despite rotational symmetry of the underlying equations of motion. This provides an explicit example of a fully closed, rotationally invariant classical-quantum system with completely positive dynamics that violates a conservation law.