What gravity mediated entanglement can really tell us about quantum gravity

Abstract: We revisit the Bose-Marletto-Vedral (BMV) table-top experimental proposal - which aims to witness quantum gravity using gravity mediated entanglement - analyzing the role of locality in the experiment. We first carry out a fully quantum modelling of the interaction of matter and gravity and then show in what way gravity mediated entanglement in the BMV experiment could be accounted for without appealing to quantum degrees of freedom of the gravitational field. We discuss what assumptions are needed in order to interpret the current BMV experiment proposals as a proof of quantum gravity, and also identify the modifications that a BMV-like experiment could have in order to serve as proof of quantum gravity without having to assume the existence of a local mediators in the gravitational field.

• The paper examines the BMV experiment to assess if gravity mediated entanglement indicates intrinsic quantum features of gravity.
• It utilizes quantum field theory to compare quantum and classical gravitational interactions, highlighting key theoretical assumptions.
• Experimental modifications, such as aligning interaction times with light-crossing intervals, are proposed to strengthen evidence for quantum gravity.

Overview of Gravity Mediated Entanglement and Quantum Gravity

The paper "What gravity mediated entanglement can really tell us about quantum gravity" scrutinizes the Bose-Marletto-Vedral (BMV) experiment aimed at detecting quantum gravity through gravity-mediated entanglement. The authors explore whether these experiments can prove the quantum nature of gravity without assuming quantum degrees within gravitational fields and offer insights into modifications that could strengthen claims about quantum gravity.

Entanglement and Quantum Gravity Experiments

The BMV Experimental Setup

The BMV proposal involves two particles in a superposition traveling along two paths, influenced solely by gravity. The concept aims for these paths to generate distinct gravitational fields which can entangle the particles.

Figure 1: Schematic representation of the BMV setup, where two particles labelled by $i=1,2$ can undergo a superposition of two trajectories, $z_{L_i}(t)$ and $z_{R_i}(t)$, corresponding to quantum states $\ket{L_i}$ and $\ket{R_i}$.

Despite technological challenges including isolating particles and minimizing decoherence, advancements are close to practical implementations. Yet, debates arise about whether gravity's capacity to entangle masses indicates its quantum nature. Arguments suggest abandoning locality or categorically defining gravity as quantum if gravitational fields entangle the particles.

Quantum Modelling of Interaction

The paper explores a quantum field theoretic model of the BMV experiment, considering weak-field quantized gravity via gravitational perturbations $\hat{h}_{\mu\nu}(x)$. Propagators from quantum field theory define interactions, distinguishing classical from quantum contributions to entanglement.

Quantum Controlled Classical Fields

The authors provide a classical field description, proposing a quantum-controlled classical model where each path corresponds to distinct classical gravitational interactions between masses, showing quantum-controlled fields can yield results similar to quantum descriptions.

Analysis of Locality and Entanglement

Locality Considerations

The paper discusses two distinct notions of locality: event locality (spacetime-based) and system locality (quantum mechanics-based). It's critical to distinguish these, especially within the context of local operations and classical communication (LOCC).

Entanglement Implications

Under conventional views influenced by LOCC arguments, if gravity entangles particles, it suggests deviations from classical descriptions. However, assuming the gravitational field as a mediator inherently links quantum information principles with spacetime characteristics—highlighting the need for assumptions about mediators.

Distinguishing Quantum Gravity

Proposed Modifications

To more definitively prove quantum gravitational behavior via the BMV experiment, modifications are recommended. Achieving interaction times proportional to light-crossing times would accentuate the quantum behavior of gravitational fields. Thus, adaptations could yield stronger evidence without relying on mediator assumptions.

Broader Context and Implications

Even with classical gravity mediating entanglement, valuable insights into quantum-gravity interactions arise. Observations affirm potential for quantum channels between masses influenced by gravity—informative for quantum gravity but distinct from proving quantum field components.

Conclusion

The review presented by the authors articulates nuances in using tabletop experiments to assert claims about quantum gravity. The distinctions lie in separating mediated entanglement from intrinsic quantum behaviors within gravity. Future adaptations to BMV experiments could yield compelling evidence aligning with theoretical predictions while enhancing understanding of fundamental spacetime interactions. Quantum-controlled models could robustly support experimental setups, suggesting intriguing paths for quantum gravity investigation.