标题： 一个1.5-查询下界用于酉合成问题 显示英文标题

标题： A 1.5-Query Lower Bound for the Unitary Synthesis Problem

摘要： 我们证明了在所谓的1.5查询设置中单位合成问题的新下界。 我们的分析表明，任何试图通过有限的预言机访问来实现任意n量子比特单位变换的尝试都需要超过分数查询阈值的资源。 这一结果将Lombardi、Ma和Wright（2023）的一次查询下界扩展到了分数查询领域，并引入了一种保守且基于链式的方法来处理中间查询复杂度。 作为结果，我们得出了密码学上的含义，表明伪随机量子态在受到1.5次查询限制的对手攻击下仍然安全。 我们的工作既提供了对分数查询复杂度的概念性澄清，也为量子密码协议的设计提供了实际见解。 显示英文摘要

摘要： We prove a new lower bound for the unitary synthesis problem in the so-called 1.5-query setting. Our analysis establishes that any attempt to implement arbitrary n-qubit unitaries via limited oracle access requires resources that exceed the fractional query threshold. This result extends the one-query lower bound of Lombardi, Ma, and Wright (2023) to the fractional query regime, and introduces a conservative and chaining-based approach to handle intermediate query complexities. As a consequence, we derive cryptographic implications, showing that pseudorandom quantum states remain secure against adversaries restricted to 1.5 queries. Our work provides both conceptual clarification of fractional-query complexity and practical insights into the design of quantum cryptographic protocols.