Operator Spreading and Information Propagation: Equivalence and Beyond

2025/05/12 by Shang, Cheng, Lu, Zhi-Guang, Kinkawa, Hayato +1 · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2505.07955

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 et al. Our results clarify the extent to which operator growth governs information flow.

Citations

• Limits to velocity of signal propagation in many-body systems: a quantum-information perspective
• Operator growth and black hole formation
• Quantum Skew Divergence
• The χ ²χ2-divergence and mixing times of quantum Markov processes
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• The Capacity of Quantum Channel with General Signal States

Cited by

• Upper bounds on the Holevo quantity arising from the fundamental entropic inequality

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