异质性的资源理论：数量化与状态转换
Resource theory of imaginarity: Quantification and state conversion
摘要：
复数在经典物理和量子物理中都有广泛的应用，是描述量子系统及其动力学行为不可或缺的组成部分。最近，量子资源理论的引入，使得量子力学和量子信息理论中对复数的系统研究成为可能。在这项工作中，我们开发的理论方法的资源理论的纠缠性，最近的进展内的纠缠和一致性理论的动机。我们研究了相似性量化，重点是几何相似性和相似性的鲁棒性，并将这些工具应用于相似性理论中的状态转换问题。此外，我们还分析了光学实验中实数运算和一般运算的复杂性，重点讨论了实现这些运算所需的非固定波片的数量。我们还讨论了局域态判别的双正交性的作用，证明了任何一对实正交纯态都可以通过局域实运算和经典通信来判别。我们的研究揭示了复数在量子物理中的重要性，证明了双态性是光学实验中的一种资源。
英文摘要：
Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. In this work we develop theoretical methods for the resource theory of imaginarity, motivated by recent progress within theories of entanglement and coherence. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Moreover, we analyze the complexity of real and general operations in optical experiments, focusing on the number of unfixed wave plates for their implementation. We also discuss the role of imaginarity for local state discrimination, proving that any pair of real orthogonal pure states can be discriminated via local real operations and classical communication. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.
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