We develop a framework to extend resource measures from one domain to a larger one. We find that all extensions of resource measures are bounded between two quantities that we call the minimal and maximal extensions. We discuss various applications of our framework. We show that any relative entropy (i.e., an additive function on pairs of quantum states that satisfies the data processing inequality) must be bounded by the min and max relative entropies. We prove that the generalized trace distance, the generalized fidelity, and the purified distance are optimal extensions. And in entanglement theory we introduce a technique to extend pure-state entanglement measures to mixed bipartite states.

中文翻译：

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资源度量及其应用的最佳扩展

我们开发了一个框架来将资源度量从一个领域扩展到更大的领域。我们发现资源度量的所有扩展都被限制在我们称为最小和最大扩展的两个数量之间。我们讨论了框架的各种应用。我们表明，任何相对熵（即满足数据处理不等式的成对量子状态上的加性函数）都必须以最小和最大相对熵为界。我们证明广义迹线距离，广义保真度和纯化距离是最佳扩展。在纠缠理论中，我们引入了一种将纯态纠缠度量扩展到混合二分态的技术。