AI 中文总结
本研究证明混合量子态学习的平均情况困难性（AHL）等价于不可有效验证的单向态生成器（IV-OWSG）的存在，还得到SWAP预言机下IV-OWSG与OWSG的分离结果，解决了该领域的一个开放问题。
AI 中文摘要
密码学与学习理论的关系长期以来是理论计算机科学基础的核心主题：密码原语可隐含学习的困难性，而学习的困难性又可用于构造密码方案。近期研究已开始在量子环境中探索类似联系，将量子态学习的平均情况困难性（AHL）与单向态生成器（OWSG）等密码原语关联起来。尽管近期在纯态方面取得了相关进展，但混合态的对应关系仍是一个开放问题。本研究证明，混合量子态学习的平均情况困难性（AHL）的存在，等价于不可有效验证的单向态生成器（IV-OWSG）的存在。由此，这将混合态AHL与EFI对关联起来；此外，作为现有结果的推论，我们在SWAP预言机下得到了IV-OWSG与OWSG之间的分离结果。
英文摘要
The relationship between cryptography and learning theory has long been a central theme in the foundations of theoretical computer science: cryptographic primitives can imply hardness of learning, while hardness of learning can in turn be used to construct cryptographic schemes. Recent works have begun exploring analogous connections in the quantum setting, relating the average-case hardness of learning quantum states (AHL) to cryptographic primitives such as one-way state generators (OWSG). Despite recent progress exploring this for pure states, the relationship for mixed states has remained an open question. In this work, we prove that the existence of AHL for mixed quantum states is equivalent to the existence of inefficiently verifiable one-way state generators (IV-OWSGs). As a consequence, this relates mixed-state AHL to EFI pairs. Moreover, as a corollary of existing results, we obtain a separation between IV-OWSGs and OWSGs relative to the SWAP oracle.
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