Tripartite measurement uncertainty in Schwarzschild space-time

TL;DR

This paper investigates how Hawking radiation affects tripartite measurement uncertainty in Schwarzschild space-time, revealing that GHZ states are more robust than W states under increasing Hawking temperature.

Contribution

It introduces a detailed analysis of measurement uncertainty in black hole backgrounds for GHZ and W states, highlighting the robustness of GHZ states against Hawking radiation.

Findings

Measurement uncertainty increases with Hawking temperature.

GHZ states are more resilient to Hawking radiation than W states.

Uncertainty behavior differs when quantum memories are in flat space versus near the black hole.

Abstract

The effect of Hawking radiation on tripartite measurement uncertainty in a Schwarzschild black hole background is analyzed in this study. Two scenarios are examined. In the first, quantum memory particles approach a Schwarzschild black hole and are positioned near the event horizon, while the particle being measured remains in the asymptotically flat region. In the second scenario, the measured particle moves toward the black hole, and the quantum memories stay in the asymptotically flat region. This study considers two initial quantum states, namely GHZ and W states. Our findings reveal that in both cases, measurement uncertainty increases steadily with rising Hawking temperature. When comparing the GHZ and W states, the GHZ state initially exhibits lower measurement uncertainty at low Hawking temperatures than the W state, indicating greater resilience to Hawking radiation. Additionally, when the quantum memories remain in the asymptotically flat region while the measured particle falls toward the black hole, the uncertainties for GHZ and W states do not align at high temperatures. The GHZ state consistently demonstrates lower measurement uncertainty, showcasing its superior robustness against Hawking radiation.