Quantum steering for different types of Bell-like states in gravitational background

TL;DR

This paper explores how quantum steering behaves for different Bell-like states near a black hole horizon, revealing that non-maximally entangled states can outperform maximally entangled ones under Hawking radiation.

Contribution

It demonstrates that non-maximally entangled states maintain steerability at high Hawking temperatures, challenging the traditional view that maximally entangled states are always superior in relativistic settings.

Findings

Fermionic steerability of maximally entangled states experiences sudden death with increasing Hawking temperature.

Non-maximally entangled states retain steerability even at infinite Hawking temperature.

Steering asymmetry can transition from two-way to one-way due to Hawking effect.

Abstract

In a relativistic framework, it is generally accepted that quantum steering of maximally entangled states provide greater advantages in practical applications compared to non-maximally entangled states. In this paper, we investigate quantum steering for four different types of Bell-like states of fermionic modes near the event horizon of a Schwarzschild black hole. In some parameter spaces, the peak of steering asymmetry corresponds to a transition from two-way to one-way steerability for Bell-like states under the influence of the Hawking effect. It is intriguing to find that the fermionic steerability of the maximally entangled states experiences sudden death with the Hawking temperature, while the fermionic steerability of the non-maximally entangled states maintains indefinite persistence at infinite Hawking temperature. In contrast to prior research, this finding suggests that quantum steering of non-maximally entangled states is more advantageous than that of maximally entangled states for processing quantum tasks in the gravitational background. This surprising result overturns the traditional idea of ``the advantage of maximally entangled steering in the relativistic framework" and provides a new perspective for understanding the Hawking effect of the black hole.