Operator Spreading and Information Propagation: Equivalence and Beyond

TL;DR

This paper explores the relationship between operator spreading and information flow in quantum systems, deriving bounds on information capacity that clarify how operator growth influences quantum information propagation.

Contribution

It provides new bounds on the Holevo capacity in terms of trace norm distance, enhancing understanding of operator growth's role in quantum information transfer.

Findings

Derived tighter bounds on Holevo capacity

Clarified the role of operator growth in information flow

Sharpened previous theoretical results

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.