发表机构
Freie Universität Berlin; Helmholtz-Zentrum Berlin für Materialien und Energie; The University of Chicago（柏林自由大学; 亥姆霍兹柏林材料能源中心; 芝加哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究明确统计伪随机性非PRU必要条件，提出区分度阈值，构造无需统计伪随机量子系综的非自适应安全PRU，还将区分度用于约束随机相位-哈达玛系综的推测伪随机性。
AI 中文摘要
伪随机性在量子信息论、统计力学和量子多体物理中被日益视为系综的关键性质，然而它呈现两种概念上不同的形式：由幺正设计体现的统计伪随机性，以及由伪随机幺正算子（PRU）刻画的计算伪随机性。这两种伪随机性形式之间的关系仍鲜为人知。现有PRU构造揭示了这种相互作用，其中将统计随机化成分——幺正设计——与经典密码原语结合以产生计算伪随机性。我们证明统计伪随机性对于计算伪随机幺正算子并非必要，方法是将现有构造中的幺正2-设计层替换为甚至不是态1-设计的系综，但其具有足够的“区分度”，我们确定该性质是任何PRU的必要条件。这产生了新的非自适应安全PRU系综，其计算伪随机性无需底层统计伪随机量子系综（如2-设计）即可获得。我们通过反聚束的纠缠类似物来刻画区分度，并用其表明区分度已捕获对PRU的相干性和虚部的约束，同时确定了后者障碍消失的广泛输入类，使得即使对于某些（最大）纠缠态也能实现实值PRU。作为应用，我们利用区分度的缺失来约束随机相位-哈达玛系综的推测伪随机性，以形成PRU。
英文摘要
Pseudorandomness is increasingly recognized as a key property of ensembles in quantum information theory, statistical mechanics, and quantum many-body physics. Yet it appears in two conceptually different forms: statistical pseudorandomness, embodied by unitary designs, and computational pseudorandomness captured by pseudorandom unitaries (PRUs). The relationship between these two forms of pseudorandomness remains surprisingly poorly understood. Existing PRU constructions reveal this interplay where a statistically randomizing ingredient, a unitary design, is combined with classical cryptographic primitives to produce computational pseudorandomness. We show that statistical pseudorandomness is not necessary for computationally pseudorandom unitaries. We do this by replacing the unitary $2$-design layer in the existing constructions with ensembles that are not even state $1$-designs, yet are sufficiently {\em distinct}, a property we identify to be necessary for any PRU. This yields new non-adaptively secure PRU ensembles whose computational pseudorandomness is obtained without an underlying statistically pseudorandom quantum ensemble, such as a $2$-design. We characterize distinctness via an entangled analogue of anticoncentration and use it to show that distinctness already captures constraints on coherence and imaginarity of PRUs, while identifying broad classes of inputs for which the latter obstruction disappears, enabling real-valued PRUs even for certain (maximally) entangled states. As an application, we use lack of distinctness to constrain the conjectured pseudorandomness of the random phase-Hadamard ensemble to form a PRU.
