Quantum Steering of Imaginarity in Schwarzschild Spacetime

ABSTRACT

We study the distribution of quantum imaginarity in Schwarzschild spacetime under Hawking radiation via imaginarity steering functionals. For bipartite systems, we analyze Werner states and general two‐qubit X‐states and find that the steering functional of physically accessible states decreases monotonically with Hawking temperature, shrinking the steerable region, whereas physically inaccessible states remain unsteerable for all temperatures. For multipartite systems, we consider general three‐qubit pure states up to local unitary equivalence and show that Hawking radiation induces a family of monogamy‐like steering inequalities with temperature‐independent bounds determined by subsystem accessibility. The corresponding maximal sum of imaginarity steering functionals decreases as the Hawking temperature increases when both subsystems are accessible, remains invariant when only one subsystem is inaccessible, and increases when both subsystems are inaccessible. These results reveal how Hawking radiation reshapes the distribution of imaginarity in relativistic spacetime.