Order-Sensitive Quantum Distinguishability in Hawking Greybody Scattering

Abstract

We study how composition order becomes operationally distinguishable when a phase-sensitive Gaussian control is applied before or after black-hole greybody scattering. The scattering process is formulated on calibrated asymptotic mode ports as a bosonic attenuation channel, and the control is a calibrated squeezing transformation. For finite-dimensional faithful families near a common faithful output, the local symmetrized Umegaki response is governed by the Bogoliubov-Kubo-Mori norm of the channel-composition defect; the corresponding bosonic problem is solved exactly at the Gaussian-state level. The exact attenuation-squeezing response yields an infrared exponent-transfer law relating greybody transmission and occupation scalings to distinguishability. For a massless scalar on Schwarzschild, matched low-frequency scattering gives an explicit fixed-partial-wave logarithmic coefficient and a locally integrable packet response. At finite squeezing, the infrared outputs approach distinct pure Gaussian supports, producing finite sandwiched Rényi divergence below unit order, logarithmic Umegaki growth at unit order, and divergence above unit order. Schwarzschild-de Sitter boundary prescriptions generate controlled source-isolated and product-horizon crossover sectors. The results apply to calibrated asymptotic-port compositions and to the reduced finite-band selected-mode realization under the stated narrowband and channel assumptions.

41 pages; 3 figures