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Does the survival and sudden death of quadripartite steering in curved spacetime truly depend on multi-directionality?

Xiaobao Liu, Wentao Liu, Si-Han Shang, Shu-Min Wu

TL;DR

This work addresses how Gaussian quadripartite steering depends on direction in the curved spacetime of a Schwarzschild black hole. By modeling Hawking radiation as a two-mode squeezing channel and using a five-mode covariance framework, the authors derive analytic expressions for both physically accessible and inaccessible steering across various partitions. They demonstrate abrupt phenomena such as sudden death and sudden birth of steering, reveal strong directional asymmetries, and show that the initial squeezing and Hawking temperature jointly shape the redistribution of steering among accessible and inaccessible sectors. The findings illuminate how black hole gravity reshapes directional quantum correlations, with potential implications for relativistic quantum information tasks near horizons.

Abstract

We systematically investigate the directional dependence of Gaussian quadripartite quantum steering and its redistribution among different modes in the background of a Schwarzschild black hole. For physically accessible sectors, we identify three distinct behaviors: (i) steering from non-gravitational to gravitational observers undergoes sudden death at maximal asymmetry with the Hawking temperature, marking the crossover from two-way to one-way steerability; (ii) steering in the opposite direction decays monotonically and vanishes only in the extreme black hole limit, highlighting its directional sensitivity to spacetime curvature; (iii) steering from hybrid gravitational-non-gravitational partitions to non-gravitational mode persists at a finite asymptotic value set by the initial squeezing parameter. Moreover, all inaccessible steerings generated by the Hawking effect exhibit an intrinsic asymmetry, with their specific behavior being strongly dependent on the steering direction.

Does the survival and sudden death of quadripartite steering in curved spacetime truly depend on multi-directionality?

TL;DR

This work addresses how Gaussian quadripartite steering depends on direction in the curved spacetime of a Schwarzschild black hole. By modeling Hawking radiation as a two-mode squeezing channel and using a five-mode covariance framework, the authors derive analytic expressions for both physically accessible and inaccessible steering across various partitions. They demonstrate abrupt phenomena such as sudden death and sudden birth of steering, reveal strong directional asymmetries, and show that the initial squeezing and Hawking temperature jointly shape the redistribution of steering among accessible and inaccessible sectors. The findings illuminate how black hole gravity reshapes directional quantum correlations, with potential implications for relativistic quantum information tasks near horizons.

Abstract

We systematically investigate the directional dependence of Gaussian quadripartite quantum steering and its redistribution among different modes in the background of a Schwarzschild black hole. For physically accessible sectors, we identify three distinct behaviors: (i) steering from non-gravitational to gravitational observers undergoes sudden death at maximal asymmetry with the Hawking temperature, marking the crossover from two-way to one-way steerability; (ii) steering in the opposite direction decays monotonically and vanishes only in the extreme black hole limit, highlighting its directional sensitivity to spacetime curvature; (iii) steering from hybrid gravitational-non-gravitational partitions to non-gravitational mode persists at a finite asymptotic value set by the initial squeezing parameter. Moreover, all inaccessible steerings generated by the Hawking effect exhibit an intrinsic asymmetry, with their specific behavior being strongly dependent on the steering direction.

Paper Structure

This paper contains 7 sections, 51 equations, 3 figures.

Table of Contents

  1. introduction
  2. Measure of Gaussian quantum steering
  3. Hawking effect in terms of effective Gaussian channel
  4. Distribution of Gaussian quadripartite steering in curved spacetime
  5. Gaussian quadripartite steering between initially correlated modes
  6. Generation of Gaussian quadripartite steering between initially uncorrelated modes
  7. CONCLUSIONS

Figures (3)

  • Figure 1: Physically accessible $1\rightarrow 3$ and $3\rightarrow 1$ steering as a function of the Hawking temperature parameter $s$ for different initial parameters $r$.
  • Figure 2: Gaussian steering asymmetries of accessible four-mode systems as functions of the Hawking temperature parameter $s$ and the initial squeezing parameter $r$.
  • Figure 3: Physically inaccessible steering and steering asymmetry as a function of the Hawking temperature parameter $s$ for a fixed initial parameter $r=1$.