Opposite post-processing orders of fermionic horizon channels and their quantum-resource monotonicity

Abstract

Relativistic quantum-information studies in noninertial and black-hole settings often determine resource behavior through explicit calculations for particular input states and state functionals, leaving unclear whether the recurring monotonic trends originate from those choices or from a common underlying structure. In this work, we formulate the effective single-mode fermionic horizon transformation as a pair of complementary exterior and interior quantum channels, corresponding respectively to the physically accessible and inaccessible sectors, and establish exact post-processing orders in opposite directions. As the relativistic channel parameter $q$ increases, the exterior channel becomes progressively degraded, whereas the interior channel is ordered in the reverse direction. These relations extend to arbitrary multipartite settings. Consequently, every state functional that is non-increasing under the corresponding intermediate maps is non-increasing in homogeneous exterior sectors and non-decreasing in homogeneous interior sectors. The framework therefore applies to broad classes of quantum resources and correlations, including entanglement and occupation-basis coherence monotones, optimized Bell-functional quantities, and contractive-divergence correlation measures. We further numerically evaluate collective coherence based on the quantum Jensen-Shannon divergence (QJSD) in the Garfinkle-Horowitz-Strominger (GHS) dilaton-black-hole spacetime, illustrating the predicted homogeneous monotonicity. The recurring trends are therefore traced to a common channel-ordering structure, while the physical setting determines the parameterization of $q$ and the resource-theoretic monotonicity determines which output-state quantities inherit the order.

11 pages, 2 figures