Adiabatic transport of qubits around a black hole

TL;DR

This paper develops a geometric framework to analyze how localized qubits evolve and decohere around a black hole, especially during quantum teleportation near the event horizon, with implications for quantum information in curved spacetime.

Contribution

It introduces a fiber bundle-based geometric structure to unify qubit states and spacetime geometry, and analyzes quantum decoherence and teleportation fidelity near black holes.

Findings

Decoherence of qubits is influenced by black hole spacetime geometry.

A formula for teleportation fidelity near a black hole is derived.

Analysis specific to Schwarzschild black holes is provided.

Abstract

We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states of a qubit and the spacetime geometry in a single framework. The quantum decoherence induced by the black hole on the qubit is analysed in this framework (the role of the dynamical and geometric phases in this decoherence is treated), especially for the quantum teleportation protocol when one qubit falls to the event horizon. A simple formula to compute the fidelity of the teleportation is derived. The case of a Schwarzschild black hole is analysed.