Quantum state texture of maximal-resource Fourier states under Hawking radiation

Abstract

Quantum state texture (QST) is a recently proposed quantum resource that characterizes the nonuniformity of a density matrix in a given computational basis. In the resource theory of QST, the Fourier states f_k are maximally resourceful states, attaining the maximum QST measure. We study the QST behavior of three maximally resourceful states in a two-mode Dirac field under Hawking radiation from a Schwarzschild black hole, using a fidelity-based measure. We consider three cases: only mode B undergoes radiation, only mode A undergoes radiation, and both modes undergo radiation simultaneously. Our results show that for single-mode radiation, if the mode unaffected by radiation is orthogonal to the single-mode textureless state, the QST of the overall output state remains maximal and is independent of the Hawking temperature; we call this phenomenon orthogonality protection. When both modes undergo radiation simultaneously, orthogonality protection vanishes, and the QST of all three Fourier states decreases with increasing Hawking temperature. Notably, the QST measure of f_3 under two-mode radiation is higher than that under only mode B radiation, indicating that QST can be redistributed among modes: QST gained by one mode under radiation can partially compensate for QST lost by the other. We further provide a general resource-theoretic explanation of orthogonality protection, showing that this phenomenon is independent of the specific form of the QST measure. These results reveal how QST degrades under Hawking radiation and provide a new perspective on the redistribution of quantum resources in black hole backgrounds.