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This paper establishes a fundamental speed limit for information scrambling in quantum systems, proving that the time required is universally at least logarithmic with respect to entanglement entropy. By refining the energy-time uncertainty principle and analyzing spectral form factors, the authors confirm the fast scrambling conjecture as an intrinsic property of quantum mechanics rather than a model-specific feature. This result provides a rigorous bound on nonequilibrium dynamics applicable to any Hamiltonian system, regardless of locality or interaction type.
Proof of a Universal Speed Limit on Fast Scrambling in Quantum Systems
arXiv:2404.15403v2 Announce Type: replace Abstract: We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in nonequilibrium quantum dynamics. (1) It sets the earliest possible time for the applicability of equilibrium statistical mechanics in a quantum system coupled to a bath at a finite temperature. (2) It proves a version of the fast scrambling conjecture, originally motivated in models associated with black holes, as a fundamental property of quantum mechanics itself. Our result builds on a refinement of the energy-time uncertainty principle in terms of the infinite temperature spectral form factor in quantum chaos. We generalize this formulation to arbitrary initial states of the bath, including finite temperature states, by mapping Hamiltonian dynamics with any initial state to nonunitary dynamics at infinite temperature. A regularized spectral form factor emerges naturally from this procedure, whose decay is universally constrained by analyticity in complex time. This establishes an exact speed limit on information scrambling by the most general quantum mechanical Hamiltonian, without any restrictions on locality or the nature of interactions.
Abstract:We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in nonequilibrium quantum dynamics. (1) It sets the earliest possible time for the applicability of equilibrium statistical mechanics in a quantum system coupled to a bath at a finite temperature. (2) It proves a version of the fast scrambling conjecture, originally motivated in models associated with black holes, as a fundamental property of quantum mechanics itself. Our result builds on a refinement of the energy-time uncertainty principle in terms of the infinite temperature spectral form factor in quantum chaos. We generalize this formulation to arbitrary initial states of the bath, including finite temperature states, by mapping Hamiltonian dynamics with any initial state to nonunitary dynamics at infinite temperature. A regularized spectral form factor emerges naturally from this procedure, whose decay is universally constrained by analyticity in complex time. This establishes an exact speed limit on information scrambling by the most general quantum mechanical Hamiltonian, without any restrictions on locality or the nature of interactions.
7+12 pages, 2+2 figures; v2: added an illustration of the bound for a random Hamiltonian, with additional figures and an expanded main text. Close to published version
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Chaotic Dynamics (nlin.CD)
arXiv:2404.15403 [quant-ph]
(or arXiv:2404.15403v2 [quant-ph] for this version)
Phys. Rev. Lett. 136, 150401 (2026)
https://doi.org/10.1103/y9z4-v641 DOI(s) linking to related resources
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