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

Si-Han Li, Si-Han Shang, Shu-Min Wu

TL;DR

The paper investigates how Hawking radiation from a Schwarzschild black hole affects quantum steering for four Bell-like states of fermionic modes shared by two observers outside the horizon. Using Dirac field quantization in Schwarzschild spacetime and analytic steering expressions, it shows that non-maximally entangled states can exhibit greater steerability than maximally entangled ones, and that the steerability of maximally entangled states can undergo sudden death as the Hawking temperature increases. Steering becomes asymmetric in curved spacetime, with transitions among two-way, one-way, and no-way steering, and the peak of steering asymmetry indicates the transition point. These results challenge the conventional view that maximally entangled steering is always advantageous in relativistic settings and provide guidance for resource selection in relativistic quantum information tasks.

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.

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

TL;DR

The paper investigates how Hawking radiation from a Schwarzschild black hole affects quantum steering for four Bell-like states of fermionic modes shared by two observers outside the horizon. Using Dirac field quantization in Schwarzschild spacetime and analytic steering expressions, it shows that non-maximally entangled states can exhibit greater steerability than maximally entangled ones, and that the steerability of maximally entangled states can undergo sudden death as the Hawking temperature increases. Steering becomes asymmetric in curved spacetime, with transitions among two-way, one-way, and no-way steering, and the peak of steering asymmetry indicates the transition point. These results challenge the conventional view that maximally entangled steering is always advantageous in relativistic settings and provide guidance for resource selection in relativistic quantum information tasks.

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.

Paper Structure

This paper contains 5 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quantification of bipartite steering
  3. Quantization of Dirac field in Schwarzschild spacetime
  4. Fermionic steering for different types of bell-like states in Schwarzschild spacetime
  5. Conclusions

Figures (2)

  • Figure 1: The fermionic steerability between Alice and Bob as functions of the Hawking temperature $T$ for different initial parameters $\gamma$ with fixed $\omega_{A}=1$ and $\omega_{B}=5$.
  • Figure 2: The fermionic steerability and steering asymmetry between Alice and Bob as functions of the Hawking temperature $T$ for different initial parameters $\gamma$ with fixed $\omega_{A}=0.1$ and $\omega_{B}=0.5$.