In quantum field theory, a classical gravitational potential can entangle two superposed masses through virtual matter exchange, so gravitationally induced entanglement is not by itself proof of quantum gravity.
Answers to a few questions regarding the BMV experiment
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abstract
We provide brief answers to a number of recurring questions about the BMV effect and the related experimental proposal (Bose et al., 2017; Marletto and Vedral, 2017). Some of these questions include alleged counter-examples to our result, stating that if gravity (or anything mediating the interaction) can create entanglement while complying with locality, then it must then be non-classical. Here we explain why these objections are not counter-examples and why our result still stands; we also explore a few other important subtleties often disregarded on a first read of our paper (Marletto and Vedral, 2017).
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Classical theories of gravity produce entanglement
In quantum field theory, a classical gravitational potential can entangle two superposed masses through virtual matter exchange, so gravitationally induced entanglement is not by itself proof of quantum gravity.