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Entanglement Propagation Velocity Spectrum (EPVS)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

Entanglement is a defining resource of quantum mechanics, yet the dynamics of how entanglement structures evolve and spread through many-body systems remains poorly quantified. Conventional studies focus on the speed of information transfer or on the growth of entanglement entropy, both of which provide limited insight into the detailed reshaping of multipartite correlations. In this work we introduce the Entanglement Propagation Velocity Spectrum, denoted v_E(omega), as a new spectral descriptor of entanglement dynamics. The EPVS captures the frequency-dependent rate at which the entanglement structure changes when a quantum system is subjected to local or global perturbations. We derive a general formulation of v_E(omega) based on the Fourier transform of time-dependent correlation functions of entanglement witnesses and show that it is directly related to the underlying spectral density of the system's Hamiltonian. By analyzing simple spin chains, harmonic lattices, and random circuit models, we demonstrate that the EPVS can distinguish between ballistic, diffusive, and localized propagation regimes, and that its high-frequency tail reveals subtle nonlocal correlations that are invisible to conventional observables. Importantly, the EPVS provides a framework for quantifying how rapidly quantum nonlocality can be engineered or degraded, with implications for quantum communication, error correction, and the study of thermalization. We conclude by discussing experimental prospects for measuring v_E(omega) in trapped-ion and superconducting qubit platforms and outline future directions where the EPVS could guide the design of next-generation quantum technologies.

DOI
10.5281/zenodo.21972715

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Quantum entanglement growth is commonly summarized by a single entropy, obscuring where correlations reside in the exponentially large Schmidt spectrum and how they form. Here, we introduce Schmidt-scale concentration and dominant Schmidt scale, two coordinates that locate the probability maximum across logarithmic windows in ordered Schmidt-rank space. Applied to quenches of a random-field spin chain, these coordinates distinguish rapid transport of the dominant scale to higher Schmidt rank at weak disorder from strongly suppressed transport despite continued logarithmic entropy growth at strong disorder. The disorder-averaged dynamics exhibit an ordered hierarchy: entropy production peaks first, spectral roughness and exact nonlocal magic peak next, and dominant-Schmidt-scale transport becomes typical only after a substantial delay. Moreover, a solvable head--tail model and controlled numerical experiments reveal the physical origin of this hierarchy: the spectral path determines the order of events, local dynamics on active exchange bonds set their early timing, and intra-subsystem many-body dressing further delays dominant-Schmidt-scale transport. These results establish the Schmidt-scale coordinates as powerful dynamical probes for uncovering fine-grained entanglement structures distinguishing entanglement production, entanglement-spectrum reorganization, and dominant-Schmidt-scale transport beyond entropy alone.
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