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This research establishes a unified resource theory linking entanglement and magic within the context of information scrambling, revealing their rigorous trade-off relations through an analytically derived maximum measure. By quantifying how unitary transformations amplify this combined metric, the study offers deeper theoretical insights into non-classical behavior that extend beyond specific scrambling scenarios to general quantumness. These findings advance fundamental understanding in quantum computing resource theories and may inform future protocols involving Pauli propagation methods.
Unified quantification of entanglement and magic in information scrambling and their trade-off relation
arXiv:2508.11969v3 Announce Type: replace Abstract: Entanglement and magic are among the most fundamental properties unique to quantum systems. Each quantity captures a different aspect of non-classical behavior, and each can be regarded as a resource within its own operational setting. However, the interrelation between them has not yet been fully clarified, and whether a more fundamental measure exists remains an open question. Addressing these issues is essential for deepening our understanding of quantumness. In this study, we establish a unified resource theory of information scrambling, consisting of two types: entanglement scrambling and magic scrambling. We introduce a measure that jointly characterizes both types of scrambling. This unified approach reveals a rigorous trade-off relation between entanglement and magic scrambling, as the exact maximum value of the proposed measure can be derived analytically. Furthermore, we quantify the scrambling capability of unitary transformations in terms of their ability to amplify this measure. We also discuss the relevance of our framework to the Pauli propagation method as a practical application. Our work provides insights into the connection between entanglement and magic that extend beyond the context of information scrambling.
Abstract:Entanglement and magic are among the most fundamental properties unique to quantum systems. Each quantity captures a different aspect of non-classical behavior, and each can be regarded as a resource within its own operational setting. However, the interrelation between them has not yet been fully clarified, and whether a more fundamental measure exists remains an open question. Addressing these issues is essential for deepening our understanding of quantumness. In this study, we establish a unified resource theory of information scrambling, consisting of two types: entanglement scrambling and magic scrambling. We introduce a measure that jointly characterizes both types of scrambling. This unified approach reveals a rigorous trade-off relation between entanglement and magic scrambling, as the exact maximum value of the proposed measure can be derived analytically. Furthermore, we quantify the scrambling capability of unitary transformations in terms of their ability to amplify this measure. We also discuss the relevance of our framework to the Pauli propagation method as a practical application. Our work provides insights into the connection between entanglement and magic that extend beyond the context of information scrambling.
arXiv:2508.11969 [quant-ph]
(or arXiv:2508.11969v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2508.11969 Focus to learn more arXiv-issued DOI via DataCite
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