Part 1 · quantum gravity
The first useful simplification is also the most revealing: the entangling content of the two-mass proposal is one nonlocal phase.
Four spatial branches
Give each mass two possible positions, |L⟩ and |R⟩, and prepare both in |+⟩. The four joint branches have different separations and therefore accumulate different gravitational phases. After removing a global phase and local single-qubit phases, only one combination remains physically nonlocal.
\[|\psi_\chi\rangle=\frac{1}{2}(|00\rangle+|01\rangle+|10\rangle+e^{i\chi}|11\rangle)\]Up to local unitaries this is exactly a controlled-phase operation, CP(χ). Its concurrence is |sin(χ/2)|: zero for a locally removable phase and maximal when χ = π modulo 2π.
What an observation would mean
The BMV proposals use spin correlations to witness entanglement between the two masses. Under their mediation assumptions, generating that entanglement would certify nonclassical features of the mediator. It would be profound physics, but it would not make this two-qubit calculation classically difficult.
Sources and reproducibility
- Bose et al., A Spin Entanglement Witness for Quantum Gravity
- Marletto & Vedral, Gravitationally Induced Entanglement
- Sabín, Digital quantum simulation of quantum gravitational entanglement
- Pastawski et al., Holographic quantum error-correcting codes
- IBM Quantum documentation: ZNE and PEA
- Public code, numerical reports and full 42-value table on GitHub
Project status: 14 August 2026. Numerical values come from the frozen public research artifacts; claim boundaries are deliberately preserved.