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On propagation of information in quantum many-body systems

The finite speed of propagation of particles and fields is a fundamental law of nature. It provides powerful constraints in relativistic physics. It is remarkable that such constraints also effectively exist in non-relativistic quantum theory, the only quantum theory with a solid mathematical foundation and physical consistency.

Publication Date: June 11, 2025

Authors: Israel Michael Sigal, Jingxuan Zhang

Abstract:

We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the many-body evolution stays, up to small leaking probability tails, within a light cone of the support of the initial conditions. This estimate is used to prove the light-cone approximation of dynamics and Lieb–Robinson-type bound, which in turn yield the results above. Our conditions cover long-range interactions. The main results of this paper as well as some key steps of the proofs were first presented in Lemm et al. (2023).

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