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Operator Spreading and Information Propagation: Equivalence and Beyond
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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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Upper bounds on the Holevo quantity arising from the fundamental entropic inequality
A general inequality bounds the Holevo quantity of any quantum ensemble by a combination of the Holevo quantities of two auxiliary ensembles plus a mean binary entropy term, yielding simple distance-based upper bounds.
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