Complete freezing of initially maximal entanglement in Schwarzschild black hole

TL;DR

This paper demonstrates that the maximal entanglement of a four-qubit cluster state remains completely unaffected by increasing Hawking temperature in a Schwarzschild black hole, challenging the belief that gravity universally degrades quantum entanglement.

Contribution

It provides the first explicit example of maximal entanglement preservation in a black hole environment, using fermionic fields and the $CL_4$ state.

Findings

Entanglement remains constant despite increasing Hawking temperature

Maximal entanglement can be preserved in curved spacetime environments

Potential for high-quality quantum resources in relativistic quantum information

Abstract

Gravitational effects associated with black holes are widely believed to universally degrade quantum entanglement, with the loss of maximal entanglement being particularly severe and even irreversible for bosonic fields. In this work, we investigate the entanglement properties of the four-qubit cluster state ($CL_4$) for fermionic fields in the curved spacetime of a Schwarzschild black hole. Remarkably, we uncover a counterintuitive phenomenon: as the Hawking temperature increases, quantum entanglement ($1$-$3$ tangle) of the $CL_4$ state remains strictly constant, indicating a ``complete freezing of initially maximal entanglement". This constitutes the first explicit example in which maximal entanglement remains perfectly preserved in a black hole environment, defying the conventional expectation that gravitational effects can only suppress maximal quantum correlations. Moreover, our results indicate that, within a relativistic framework, the $CL_4$ state constitutes a high-quality quantum resource with potential applications in relativistic quantum information processing, and may significantly improve the performance of such protocols.