Can the latent signatures of quantum superposition be detected through correlation harvesting?

In this paper, we explore correlation harvesting in quantum superposition, specifically focusing on the entanglement and mutual information extracted by two Unruh-DeWitt detectors interacting with a quantum field in a mass-superposed BTZ black hole spacetime. Our findings reveal that the superposed nature of spacetime induces constructive interference between the field modes that can significantly enhance the entanglement harvesting relative to a single spacetime background. In contrast to entanglement, the mutual information obtained in spacetime superposition is influenced by the proper distance between the two detectors. While the mutual information harvested in a superposed spacetime remains lower than that in a single spacetime when the proper distance between detectors is small, it exceeds that in a single spacetime for specific mass ratios as the distance increases. Notably, we find that both entanglement and mutual information harvesting reach their maxima when the final spacetime superposition state is conditioned to align with the initial spacetime state.

💡 Research Summary

This paper investigates whether the presence of a quantum superposition of spacetime geometries leaves observable signatures in the process of correlation harvesting. The authors consider a pair of Unruh–DeWitt (UDW) detectors that interact locally with a massless scalar field living on a background that is a coherent superposition of two non‑rotating, chargeless BTZ black holes with different masses M₁ and M₂. The field is constructed by automorphic identification of AdS₃, yielding Wightman functions W_{M_i}^{BTZ} for each mass and a cross‑term W_{M₁M₂}^{BTZ} that encodes interference between the two geometries.

The detectors are static, switched on simultaneously with a Gaussian profile of width σ, and have identical energy gaps Ω. The interaction Hamiltonian is linear in the field and proportional to a small coupling λ. The total system (detectors + field + spacetime) is prepared in a product of detector ground states, the field vacuum, and a spacetime superposition |s_i⟩ = cosθ|M₁⟩ + sinθ|M₂⟩. After evolution to order λ², the detectors are post‑selected on a final spacetime state |s_f⟩ = cosφ|M₁⟩ + sinφ|M₂⟩, which implements a conditional measurement on the control qubit that encodes the geometry.

Tracing out the field yields a reduced two‑detector density matrix ρ_AB whose diagonal entries contain the individual excitation probabilities P_A, P_B, while the off‑diagonal entries contain non‑local terms M (responsible for entanglement) and L_AB (relevant for total correlations). These quantities are expressed as double integrals of the appropriate Wightman functions along the detector worldlines, weighted by the switching functions and the coefficients a = cosθ cosφ, b = sinθ sinφ. The cross‑Wightman function introduces a dependence on the mass ratio √(M₂/M₁); resonant enhancements appear whenever this ratio is a rational number, reflecting constructive interference of field modes in the compact AdS topology.

Entanglement is quantified by the concurrence C = 2 max