Impact of the Hawking Effect on the Fully Entangled Fraction of Three-qubit States in Schwarzschild Spacetime

TL;DR

This paper explores how Hawking radiation influences the fully entangled fraction in three-qubit states within Schwarzschild spacetime, revealing both positive and negative effects depending on initial states and state types.

Contribution

It extends previous work by analyzing the Hawking effect on tripartite entangled states, showing its dual impact on the fully entangled fraction in Schwarzschild spacetime.

Findings

Hawking effect can both decrease and increase FEF in tripartite states.

For W-like states, Hawking effect always positively impacts FEF.

Impact depends on initial state selection and type of tripartite state.

Abstract

Wu et al. [J. High Energ. Phys. 2023, 232 (2023)] first found that the fidelity of quantum teleportation with a bipartite entangled resource state, completely determined by the fully entangled fraction (FEF) characterized by the maximal fidelity between the given quantum state and the set of maximally entangled states, can monotonically increase in Schwarzschild spacetime. We investigated the Hawking effect on the FEF of quantum states in tripartite systems. In this paper, we show that the Hawking effect of a black hole may both decrease and increase the FEF in Schwarzschild spacetime. For an initial X-type state, we found that the Hawking effect of the black hole has both positive and negative impacts on the FEF of Dirac fields, depending on the selection of initial states. For an initial W-like state, the Hawking effect of the black hole has only a positive impact on the FEF of Dirac fields, independent of the selection of initial states. Our results provide an insightful view of quantum teleportation in multipartite systems under the influence of Hawking effects, from the perspective of quantum information and general relativity.