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

TL;DR

The paper investigates whether latent quantum-gravity features in spacetime can be detected via correlation harvesting by two Unruh-DeWitt detectors in a mass-superposed BTZ background. It develops a formalism for a quantum field on a superposed geometry using an automorphic field and conditioned Wightman functions, then analyzes a pair of static detectors coupled to this field with a Dyson expansion to second order in the coupling. The main findings are that spacetime superposition induces constructive interference that significantly enhances entanglement harvesting, while mutual information harvesting shows a more nuanced dependence on detector separation and spacetime-control alignment; both maximal quantum correlations occur when the measured spacetime control matches the initial superposition state. These results extend previous Minkowski-space insights to curved backgrounds and highlight how quantum gravitational features can imprint on relativistic quantum information processing. The work suggests future directions, including exploring quantum discord harvesting and more general dynamical or higher-dimensional spacetimes to probe quantum gravity phenomenology operationally.

Abstract

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.

Figures (7)

• Figure 1: Transition probability of the individual detector as a function of $\sqrt{M_2/M_1}$ with parameters $l=10\sigma$, $r_D=10\sigma$, $\sigma\Omega=0.01$, and $\zeta=1$. The measurement basis corresponding to the relevant plot is indicated by the legend. The dashed vertical lines are at rational values of $\sqrt{M_2/M_1}$ (e.g. 1, 1.2, 1.5).
• Figure 2: The concurrence $\mathcal{C}(\rho_{AB})/\lambda^{2}$ between two detectors in the superposed BTZ spacetime as a function of $\sqrt{M_2/M_1}$ is plotted for different values of $\zeta$ with parameters $l=10\sigma$, $r_A=10\sigma$, $r_B=11\sigma$, $\sigma\Omega=0.01$, and $\theta=\varphi=\frac{\pi}{4}$. Vertical dashed lines were added for distinctive peaks at rational values (e.g. 1, 1.2, 1.5).
• Figure 3: The concurrence $\mathcal{C}(\rho_{AB})/\lambda^{2}$ between two detectors in the superposed BTZ spacetime as a function of $\sqrt{M_2/M_1}$ is plotted for different values of $r_B$ with parameters $l=10\sigma$, $\sigma\Omega=0.01$, and $\theta=\varphi=\frac{\pi}{4}$.
• Figure 4: The concurrence $\mathcal{C}(\rho_{AB})/\lambda^2$ for superposed spacetime, plotted as a function of $\theta$ and $\varphi$, exhibits a maximum near $\theta = \varphi$. We use parameters $l=10\sigma$, $\sqrt{M_2/M_1} =1.5$, $r_A=10\sigma$, $r_B=11\sigma$, and $\sigma\Omega=0.01$.
• Figure 5: The mutual information $\mathcal{I}(\rho_{AB})/\lambda^{2}$ between two detectors in the superposed BTZ spacetime as a function of $\sqrt{M_2/M_1}$ is plotted for different values of $r_B$ with parameter $l=10\sigma$, $\sigma\Omega=0.01$, and $\theta=\varphi=\frac{\pi}{4}$.