Matter-Field Exchange Generates Entanglement, Not Classical Gravity

Abstract

Aziz and Howl have argued that a hybrid theory with quantum matter and a classical gravitational field can generate entanglement between two massive systems. In their construction, the branch-dependent contribution appears at fourth order through propagators of the quantum matter field in a fixed classical gravitational potential. We analyse this mechanism within the same perturbative QFT framework and show that the effect should not be interpreted as classical gravity mediating entanglement in the sense relevant to BMV-type witnesses. The non-separable term relies on a quantum-matter exchange channel between the two interferometers and is present only when the two systems are modelled as excitations of the same matter field. If distinct, non-interconverting matter fields describe the systems, the corresponding cross-propagator is absent and the Aziz-Howl entangling diagram vanishes. The effect relies on coherent propagation amplitudes of the quantum matter field between the two interferometers, together with postselection onto the original localised branch subspace. Moreover, the inference of entanglement is made after projecting the full QFT evolution onto a restricted final subspace containing the original localised $N$-particle branch states. This projection removes precisely the sectors that would record matter-field contamination, mode deformation, or exchange between the two interferometers. We therefore argue that the Aziz-Howl mechanism is a matter-sector cross-talk effect in a classical background, not entanglement mediated by classical gravitational degrees of freedom. Having identified the channel responsible for the Aziz-Howl contribution, we predict that it can be eliminated by using distinct, non-interconverting matter species in the two interferometers, or by inserting a barrier that suppresses matter-field propagation between them.