Spatiotemporal entanglement of the vacuum

Abstract

We demonstrate that the future and left Rindler wedges of Minkowski spacetime are entangled, leading to the Unruh effect. Similarly, the past and right Rindler wedges are also entangled. We propose a protocol to extract this entanglement using two two-state detectors located in the past and right Rindler wedges. By scaling the detector transition frequencies inversely with Minkowski time, entanglement from the quantum field is transferred to the detectors, suggesting they may support quantum teleportation via the vacuum. Our protocol can be implemented with current quantum systems, such as flux-tunable transmon qubits. This research provides new insights into the entanglement properties of spacetime and hints at practical applications for secure quantum information transfer using the vacuum state of a quantum field.

Figures (2)

• Figure 1: Minkowski spacetime split into four wedges by the null horizons corresponding to $U=0$ and $V=0$. Worldlines of constant $\xi$ are hyperbolic trajectories. A uniformly accelerated observer traces a hyperbolic trajectory of $\xi= 0$.
• Figure 2: Schematic representation of the light cones of null separated observers $O_1$ (solid blue) and $O_2$ (solid red) in Minkowski spacetime. The trajectories of past and right detectors in the reference frame of $O_1$ are shown as blue and red curves, respectively, with arrows indicating forward evolution in time. In this frame, past detector evolves asymptotically towards the origin, whilst right detector follows a hyperbolic path. The window functions ${\cal E}$ are shown as dashed lines as function of each observers coordinate time. The peaks in ${\cal E}$ indicate regions of spacetime where $O_i$'s detector is active. In this schematic, note that the detector of $O_2$ is active in the future light cone of $O_2$, corresponding to the right Rindler wedge of $O_1$.