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On propagation of information in quantum mechanics and maximal velocity bounds

The study of evolution of information in condensed matter physics is an active, robust area of research with many profound results. At the same time, perhaps due to the difficulty of experimental implementation, with the exception of a few works on quantum open systems, this fundamental issue was not tackled in the original setting of quantum mechanics, i.e. at zero particle density. In this paper, we address this subject in a systematic way.
On propagation of information article

Publication Date: February 7, 2025

Authors: Israel Michael Sigal and Xiaoxu Wu

Abstract:

We revisit key notions related to the evolution of quantum information in few-body quantum mechanics (fbQM) and, for a wide class of dispersion relations, prove uniform bounds on the maximal speed of propagation of quantum information for states and observables with exponential error bounds. Our results imply, in particular, a fbQM version of the Lieb–Robinson bound, which is known to have wide applications in quantum information sciences. We propose a novel approach to proving maximal speed bounds.

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