发表机构
Department of Informatics, Faculty of Information Science and Electrical Engineering, Kyushu University; JST, FOREST（九州大学信息科学与电气工程学院信息系; 日本科学技术振兴机构，FOREST项目）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出统一理论，研究有限群不对称性与多种资源理论的组合，发现转换率由对称性信息可访问性决定，组合不增加成本，并扩展至基本操作对称性及ergotropy分析。
AI 中文摘要
资源理论为量化量子态的性质（如纠缠、魔法性、非热性和不对称性）提供了通用框架，这些性质在量子科学中面临的各种约束下被视为资源。由于现实环境通常同时施加多种约束，研究组合这些约束的多资源理论非常重要。其中，与不对称性的组合尤为自然，因为对称性在物理学中是基础且普遍存在的。在此，我们发展了一个一般理论，以统一的方式处理有限群不对称性与广泛资源理论的组合。我们的关键观察是，组合两种约束的效果由底层资源理论下对称性信息的可访问性决定：即转换所需的信息是否能从输入中提取并用于控制自由操作。如果这能以渐近消失的误差完成，我们证明组合理论的转换率等于两个组成理论转换率中的较小者，因此组合它们不会产生额外成本。这一条件适用于任意混合多体态上的LOCC、Clifford对称性下多量子比特系统的魔法态转换以及Gibbs保持操作。热操作，由于是时间平移协变的，只能访问有限的对称性信息，从而在两个对称性之间产生额外的兼容性条件。我们还分析了施加在基本操作而非仅最终通道上的对称性。我们在适当假设下为LOCC和热操作建立了类似结果，并为对称性由Pauli算子表示的魔法性建立了类似结果。最后，我们证明有限群对称性不会减少每份的渐近ergotropy，因此不会引入新的完全被动态。
英文摘要
Resource theories provide a universal framework for quantifying properties of quantum states, such as entanglement, magic, athermality, and asymmetry, as resources under various constraints encountered in quantum science. Since realistic settings typically impose several constraints at once, it is important to study multi-resource theories that combine them. Among these, combinations with asymmetry are especially natural, as symmetry is fundamental and ubiquitous in physics. Here we develop a general theory that treats combinations of finite-group asymmetry with a broad range of resource theories in a unified manner. Our key observation is that the effect of combining the two constraints is governed by the accessibility of symmetry information under the underlying resource theory: whether the information needed for the conversion can be extracted from the input and used to control free operations. If this can be done with asymptotically vanishing error, we show that the conversion rate of the combined theory equals the smaller of the rates of the two constituent theories, so combining them incurs no additional cost. This condition holds for LOCC on arbitrary mixed multipartite states, magic-state conversion of multiqubit systems under Clifford symmetries, and Gibbs-preserving operations. Thermal operations, being time-translation covariant, can access only limited symmetry information, giving an additional compatibility condition between the two symmetries. We also analyze symmetry imposed on elementary operations rather than only on the resulting channel. We establish analogous results for LOCC and thermal operations under suitable assumptions, and for magic when the symmetry is represented by Pauli operators. Finally, we show that finite-group symmetry does not reduce the asymptotic ergotropy per copy and hence introduces no new completely passive states.
Comments66 pages, 1 figure
