Nonlocal Advantage of Quantum Imaginarity in Schwarzschild Spacetime

Black hole spacetimes provide a natural setting for quantum systems in curved spacetime, where effects such as Hawking radiation arise from event horizons. In this work, we investigate the impact of Hawking radiation on quantum imaginarity in Schwarzschild spacetime, focusing on nonlocal advantage of quantum imaginarity (NAQI) and assisted imaginarity distillation. For NAQI, Hawking radiation induces opposite temperature dependence of the NAQI gap in the two regions, decreasing in the physically accessible region and increasing in the physically inaccessible region. Consequently, the gap can cross zero only in the accessible region, leading to the disappearance of NAQI at sufficiently high temperature, while it remains negative in the inaccessible region. For assisted imaginarity distillation, the fidelity decreases with temperature in the physically accessible region and increases in the physically inaccessible region, resulting in reduced and enhanced distillation capability, respectively. These results reveal distinct operational behaviors of physically accessible and inaccessible regions under relativistic effects, providing insight into quantum imaginarity in
curved spacetime.