Equivalence of quantum resources under ergodic dynamics

• URL: http://arxiv.org/abs/2608.15197v1
• Date: Sat, 15 Aug 2026 12:27:58 GMT
• Title: Equivalence of quantum resources under ergodic dynamics
• Abstract summary: We show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom.<n>For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures.<n>We derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.

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