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Tripartite quantum steering in Schwarzschild spacetime

Guang-Wei Mi, Xiaofen Huang, Tinggui Zhang

TL;DR

This work analyzes how Hawking radiation in Schwarzschild spacetime affects tripartite quantum steering among three observers initially sharing a GHZ state. By quantizing a Dirac field and employing a systematic framework for steering in X-type states, it derives explicit steering measures and asymmetries for all directional partitions across scenarios with three, two, or one physically accessible modes. The main findings show that Hawking radiation can suppress steering in the fully accessible case while exhibiting dual effects (enhancement in some directions, suppression in others) when fewer modes are accessible, and it can significantly enhance steering in the single-access case. The results reveal phase-boundary signatures via steering asymmetry and provide observable fingerprints of Hawking effects in quantum steering, advancing understanding of quantum correlations in curved spacetime.

Abstract

We investigate the effects of Hawking radiation on quantum steering and steering asymmetry in a tripartite system embedded in Schwarzschild spacetime. All tripartite steering types were classified,comprising three "1 to 2" and three "2 to 1" steering cases. Through a systematic analysis of all physically relevant scenarios (including accessible and inaccessible modes), we classify three canonical scenarios with one, two and three physically accessible modes. In the scenario of three physically accessible modes, Hawking radiation disrupts quantum steering, with the maximum steering asymmetry during the two-way steering to one-way steering transition precisely demarcating the phase boundary between these regimes. For two physically accessible modes, Hawking radiation exhibits dual behavior: enhancing the steering from Alice and Bob to anti-Charlie under certain parameters while suppressing it under others, while net strengthening other steering types. When considering one physically accessible mode, the Hawking effect of the black hole significantly enhances quantum steering. These findings provide new insights into quantum correlations in curved spacetime and establish observable signatures of Hawking effects in quantum steering phenomena.

Tripartite quantum steering in Schwarzschild spacetime

TL;DR

This work analyzes how Hawking radiation in Schwarzschild spacetime affects tripartite quantum steering among three observers initially sharing a GHZ state. By quantizing a Dirac field and employing a systematic framework for steering in X-type states, it derives explicit steering measures and asymmetries for all directional partitions across scenarios with three, two, or one physically accessible modes. The main findings show that Hawking radiation can suppress steering in the fully accessible case while exhibiting dual effects (enhancement in some directions, suppression in others) when fewer modes are accessible, and it can significantly enhance steering in the single-access case. The results reveal phase-boundary signatures via steering asymmetry and provide observable fingerprints of Hawking effects in quantum steering, advancing understanding of quantum correlations in curved spacetime.

Abstract

We investigate the effects of Hawking radiation on quantum steering and steering asymmetry in a tripartite system embedded in Schwarzschild spacetime. All tripartite steering types were classified,comprising three "1 to 2" and three "2 to 1" steering cases. Through a systematic analysis of all physically relevant scenarios (including accessible and inaccessible modes), we classify three canonical scenarios with one, two and three physically accessible modes. In the scenario of three physically accessible modes, Hawking radiation disrupts quantum steering, with the maximum steering asymmetry during the two-way steering to one-way steering transition precisely demarcating the phase boundary between these regimes. For two physically accessible modes, Hawking radiation exhibits dual behavior: enhancing the steering from Alice and Bob to anti-Charlie under certain parameters while suppressing it under others, while net strengthening other steering types. When considering one physically accessible mode, the Hawking effect of the black hole significantly enhances quantum steering. These findings provide new insights into quantum correlations in curved spacetime and establish observable signatures of Hawking effects in quantum steering phenomena.
Paper Structure (10 sections, 2 theorems, 99 equations, 3 figures)

This paper contains 10 sections, 2 theorems, 99 equations, 3 figures.

Table of Contents

  1. Introduction
  2. QUANTIZATION OF DIRAC FIELD IN SCHWARZSCHILD BLACK HOLE
  3. Quantification of the Tripartite Quantum Steering
  4. Tripartite Quantum Steering in the Schwarzschild Black Hole
  5. A. Three physically accessible modes
  6. B. Two physically accessible modes
  7. C. One physically accessible mode
  8. Conclusion
  9. APPENDIX A: The steering from A to BC and BC to A
  10. APPENDIX B: The steering from B to CA and CA to B

Key Result

Lemma 1

(Observation 3 of Ref. D.Das.2019) For any qudit-qubit state $\rho_{AB}$ shared between Alice and Bob, define another new qudit-qubit state $\tau_{AB}$ given by where $\tilde{\rho^{1}}_{AB}=\rho_{A}\otimes \frac{\mathbb{I}_{2}}{2}$ with $\rho_{A}=Tr_{B}[\rho_{AB}]=Tr_{B}[\tau^{1}_{AB}]$ being the reduced state (qudit) at Alice¡¯s side and $\mathbb{I}_{2}$ is the $2\times2$ identity matrix. If $\t

Figures (3)

  • Figure 1: The quantum steering and steering asymmetry of $\rho^{H}_{ABC}$ as functions of the black hole Hawking temperature $T$ with fixed $\omega=1$ and three different values of the parameter $\alpha$: $\alpha=\frac{1}{4}$, $\alpha=\frac{1}{2}$ and $\alpha=\frac{1}{\sqrt{2}}$.
  • Figure 2: The quantum steering and steering asymmetry of $\rho^{H}_{ABc}$ as functions of the black hole Hawking temperature $T$ with fixed $\omega=1$ and three different values of the parameter $\alpha$: $\alpha=\frac{1}{4}$, $\alpha=\frac{1}{2}$ and $\alpha=\frac{1}{\sqrt{2}}$.
  • Figure 3: The quantum steering and steering asymmetry of $\rho^{H}_{Abc}$ as functions of the black hole Hawking temperature $T$ with fixed $\omega=1$ and three different values of the parameter $\alpha$: $\alpha=\frac{1}{4}$, $\alpha=\frac{1}{2}$ and $\alpha=\frac{1}{\sqrt{2}}$.

Theorems & Definitions (2)

  • Lemma 1
  • Lemma 2