发表机构
Okinawa Institute of Science and Technology Graduate University; INESC-ID, Instituto Superior Técnico, Universidade de Lisboa（冲绳科学技术大学院大学; 葡萄牙里斯本大学高等技术学院INESC-ID）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究通过EFI对建立伪纠缠与计算密码学最小假设之间的联系，证明特定操作性定义下伪纠缠的存在等价于EFI对的存在，为密码学提供新视角并搭建两领域桥梁。
AI 中文摘要
伪纠缠与计算纠缠理论的问世，推动了计算机科学与信息论交叉领域的一波研究浪潮。与此同时，受伪随机态引入的启发，计算密码学也经历了实质性发展，并确立了量子密码学所需计算难度的基线，其中EFI对作为核心原语应运而生。我们通过EFI对研究伪纠缠与计算密码学之间的联系，旨在使计算纠缠理论产生的资源能够应用于密码学领域。为此，我们建立了伪纠缠的操作性实例与计算密码学最小假设层级之间的关系。我们证明，在两种不同的操作性定义下，具有高效态生成的伪纠缠的存在性是EFI对存在的充分条件。结合先前已确立的结果（即在第二种定义下逆命题也成立），我们得以进一步证明二者的等价性。这将伪纠缠置于密码学中其他最小假设之列，不仅为这一基本问题提供了替代视角，还架起了一座桥梁，使两个领域的洞见得以相互借鉴。在证明这些定理的过程中，我们引入并展示了量子信息与计算纠缠理论中的技术性引理，将计算纠缠度量与态间距离相关联，为两族态的混合在给定其态间成对距离时建立了区分条件，并首次证明了计算纠缠度量的连续性关系。
英文摘要
The advent of pseudoentanglement and computational entanglement theory bootstrapped a wave of research at the intersection of computer science and information theory. In parallel, computational cryptography has undergone substantial development, prompted by the introduction of pseudorandom states and followed by the establishment of a baseline for the computational hardness required for quantum cryptography, from which EFI pairs emerge as a central primitive. We study the connection between pseudoentanglement and computational cryptography through EFI pairs. Our goal is to enable the use of resources arising from computational entanglement theory in the field of cryptography. For this, we establish the relation between operational instances of pseudoentanglement and the hierarchy of minimal assumptions for computational cryptography. We show that the existence of pseudoentanglement under two different operational definitions, with efficient state generation, is a sufficient condition for the existence of EFI pairs. Combined with a previously established result that the converse also holds under the second definition, this allows us to also demonstrate their equivalence. This places pseudoentanglement alongside other minimal assumptions in cryptography, not only offering an alternative perspective on this fundamental problem, but also building a bridge that allows insights from either area to inform the other. While proving these theorems, we introduce and demonstrate technical lemmas in quantum information and computational entanglement theory, relating the computational entanglement measures to the distance between states, establishing distinguishing conditions for mixtures of two families given pairwise distances between their states, and demonstrating the first continuity relation for a computational entanglement measure.
