Wormhole-Induced correlation: A Link Between Two Universes

TL;DR

This work investigates how a BTZ wormhole with a null-like throat influences quantum correlations harvested from vacuum fluctuations by two Unruh-DeWitt detectors. Using a perturbative detector-field interaction and a topological-image construction of the Wightman function, it shows that the wormhole enhances mutual information between detectors located on opposite sides, with maximal correlations at image-symmetric positions. The analysis reveals genuine nonlocal quantum content through the nonlocal term $|\mathcal{M}|$ exceeding the local noise $\xi$, enabling nonzero concurrence $C_{AB}$ near symmetry, while no communication between universes is allowed. The study provides a concrete link between spacetime topology and quantum nonlocality, suggesting that wormhole geometries can act as geometric bridges for quantum correlations and inviting cross-framework comparisons in quantum gravity theories.

Abstract

Motivated by the profound connection between quantum mechanics and spacetime geometry, particularly the conjectured correspondence between wormholes and quantum entanglement as proposed in the ER=EPR framework, this study investigate the influence of wormhole geometries on quantum information extraction. We examine the correlation-specifically mutual information (MI) and entanglement-extracted by two Unruh-DeWitt (UDW) detectors from the quantum vacuum field in the presence of a BTZ wormhole featuring a null-like throat, also known as an Einstein-Rosen bridge. First, we analyze how the detector's position relative to the wormhole throat and the throat's size affect the extracted MI. Our results indicate that the wormhole enhances MI extraction, with maximal MI achieved when the detectors are located at specific image-symmetric points connected by the wormhole. By analyzing the behavior of the nonlocal contribution term and the classical noise term, it is found that the correlations extracted contain genuine non-classical components. This work highlights the feasibility of extracting quantum correlations through null-like wormhole geometries and provides a novel perspective for probing the potential relationship between spacetime topology and the nonlocal characteristics of quantum mechanics.

Figures (7)

• Figure 1: (a) Spacetime embedding graph of the BTZ null-like wormhole, depicted at a constant time slice $t$ = const. The upper and lower regions represent two congruent universes connected by the central circle, which represents the throat of the wormhole. The wormhole vanishes when the radius $u_0$ approaches zero. (b) Schematic representation of the throat size and the arrangement of UDW detectors during our correlation harvesting process. Detectors Alice and Bob are positioned on opposite sides of the wormhole, initially in their ground states, uncorrelated, and possessing the same energy gap $\Omega_A=\Omega_B=\Omega$.
• Figure 2: The Penrose diagram of the extended BTZ spacetime. Regions I and IV as two universes connected via an event horizon. Regions II and III represent the interiors of the black hole and white hole, respectively. The wavy lines at the top and bottom denote the spacelike infinity ($r=0$), while special spacelike hypersurfaces ($U = -V$ or $T = 0$) traversing both universes are indicated by yellow dashed lines.
• Figure 3: Plot of extracted MI $I_{AB}/\tilde{\lambda}^2$ (depicted in red) and TP $L_{DD}/\tilde{\lambda}^2$ (in blue) versus the size of the throat $u_0/\sigma$. Alice and Bob are symmetrically distributed around the throat at three different distances, represented by different line types: $u/\sigma=1$ (solid), $u/\sigma=0.1$ (dashed), and $u/\sigma=0.01$ (dotdashed). The upper-right subfigure is plotted for the last two distributions with a larger value of $u_0/\sigma$. Parameters are $\Omega \sigma = 1$, $M = 10^{-2}$.
• Figure 4: Plot of the extracted MI (solid purple) and TP (dashed blue). The particle detectors are symmetrically placed. From (a) to (c), the size of the wormhole throat is set to 0.01, 0.1, and 1, respectively. Here $\Omega \sigma = 1$, $M= 10^{-2}$.
• Figure 5: The plots illustrate the extracted MI (solid purple), TP (dashed blue), and the off-diagonal element $L_{AB}$ (dashed green). In panel (a), the wormhole throat is set to 0.5 and detector Bob is fixed at $u_0/\sigma = -0.2$, while in panel (b), the size is set to 2 and Bob is fixed at $u_0/\sigma = -0.7$, with Alice positioned at various locations. The insets emphasize the regions of peak MI, with the red dashed line marking the position symmetrical to Bob. Parameters are set as $\Omega \sigma = 1$ and $M = 10^{-2}$.