Operator Spreading and Information Propagation: Equivalence and Beyond

Cheng Shang; Zhi-Guang Lu; Hayato Kinkawa; Tomotaka Kuwahara

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arXiv · 2505.07955

Operator Spreading and Information Propagation: Equivalence and Beyond

Cheng Shang·Zhi-Guang Lu·Hayato Kinkawa·Tomotaka Kuwahara

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Abstract

We investigate the quantitative relationship between operator spreading and classical information propagation in quantum systems. Focusing on a bi-partite quantum channel, we derive new upper and lower bounds on the Holevo capacity, a typical information measure, in terms of the trace norm distance between output states, sharpening earlier results by Bravyi \textit{et al}. Our results clarify the extent to which operator growth governs information flow.

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Cheng Shang, Zhi-Guang Lu, Hayato Kinkawa, Tomotaka Kuwahara. 2025-05-12. Operator Spreading and Information Propagation: Equivalence and Beyond. https://arxiv.org/abs/2505.07955

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