Mao Kaneyasu | Searcharxiv

arXiv2025

Unified quantification of entanglement and magic in information scrambling and their trade-off relation

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.

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arXiv2023

Quantum Otto cycle under strong coupling

Quantum heat engines are often discussed under the weak coupling assumption that the interaction between the system and the reservoirs is negligible. Although this setup is easier to analyze, this assumption cannot be justified on the quantum scale. In this study, a quantum Otto cycle model that can be generally applied without the weak coupling assumption is proposed. We replace the thermalization process in the weak coupling model with a process comprising thermalization and decoupling. The efficiency of the proposed model is analytically calculated and it indicates that when the contribution of the interaction terms is neglected in the weak interaction limit, it reduces to that of the earlier model. The sufficient condition for the efficiency of the proposed model not to surpass that of the weak coupling model is that the decoupling processes of our model have a positive cost. Moreover, the relation between the interaction strength and the efficiency of the proposed model is numerically examined using a simple two-level system. Furthermore, we show that our model's efficiency can surpass that of the weak coupling model under particular cases. From analyzing the majorization relation, we also find a design method of the optimal interaction Hamiltonians which are expected to provide the maximum efficiency of the proposed model. Under these interaction Hamiltonians, the numerical experiment shows that the proposed model achieves higher efficiency than that of its weak coupling counterpart.

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