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This paper investigates the fundamental relationship between quantum scrambling and entanglement dynamics within chaotic regimes using Rosenzweig-Porter ensembles. By introducing time-integrated spread complexity metrics, it establishes a monotonic inverse correlation with state fidelity as systems transition from integrability to chaos under operator perturbations. The work advances theoretical understanding of quantum ergodicity without proposing immediate applications for near-term hardware or algorithms.
Scrambling of Entanglement from Integrability to Chaos: Bootstrapped Time-Integrated Spread Complexity
arXiv:2604.14224v5 Announce Type: replace Abstract: A physical relationship for the combination of scrambling via spread complexity and entanglement is characterized by the fidelity of quantum unitary dynamics. Newly introduced time-integrated quantities for the degree of quantum ergodicity captures state spreading from initial to late times under physically plausible operator perturbations. Using bootstrapped Hamiltonian realizations as a perturbation scheme shown to be a powerful testbed. Selecting maximally entangled state as a starting state captures the scrambling of entanglement in this setting. For this reason, we utilize the Rosenzweig-Porter ensembles across different ergodic regimes. Computed integrated spread complexity and associated integrated quantum state fidelity displays a monotonic inverse relationship for maximally entangled states from integrability to chaos.
Abstract:A physical relationship for the combination of scrambling via spread complexity and entanglement is characterized by the fidelity of quantum unitary dynamics. Newly introduced time-integrated quantities for the degree of quantum ergodicity captures state spreading from initial to late times under physically plausible operator perturbations. Using bootstrapped Hamiltonian realizations as a perturbation scheme shown to be a powerful testbed. Selecting maximally entangled state as a starting state captures the scrambling of entanglement in this setting. For this reason, we utilize the Rosenzweig-Porter ensembles across different ergodic regimes. Computed integrated spread complexity and associated integrated quantum state fidelity displays a monotonic inverse relationship for maximally entangled states from integrability to chaos.
9 pages, 4 Figures, new sectioning, text improvements and new reference to FOTOCs. Notebooks and dataset are available on Zenodo: this https URL
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2604.14224 [quant-ph]
(or arXiv:2604.14224v5 [quant-ph] for this version)
From: Mehmet A. Süzen PhD [view email] [v1] Tue, 14 Apr 2026 13:16:20 UTC (125 KB) [v2] Fri, 24 Apr 2026 07:00:53 UTC (130 KB) [v3] Sun, 17 May 2026 12:51:10 UTC (147 KB) [v4] Mon, 25 May 2026 08:56:12 UTC (142 KB) [v5] Mon, 3 Aug 2026 07:46:22 UTC (171 KB)
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