Trapdoor claw-free functions (TCFs) are immensely valuable in cryptographic interactions between a classical client and a quantum server. Typically, a protocol has the quantum server prepare a superposition of two-bit strings of a claw and then measure it using Pauli-$X$ or $Z$ measurements. In this paper, we demonstrate a new technique that uses the entire range of qubit measurements from the $XY$-plane. We show the advantage of this approach in two applications. First, building on (Brakerski et al. 2018, Kalai et al. 2022), we show an optimized two-round proof of quantumness whose security can be expressed directly in terms of the hardness of the LWE (learning with errors) problem. Second, we construct a one-round protocol for blind remote preparation of an arbitrary state on the $XY$-plane up to a Pauli-$Z$ correction.

翻译：陷门单射函数（TCFs）在经典客户端与量子服务器之间的密码学交互中具有极高价值。典型的协议中，量子服务器制备一对位串重叠态的叠加态，然后通过Pauli-$X$或$Z$测量进行测量。本文提出一种利用$XY$平面全范围量子比特测量的新技术。我们展示了该方法在两个应用中的优势。首先，基于(Brakerski等，2018；Kalai等，2022)的工作，我们提出一种优化的两轮量力证明，其安全性可直接表述为LWE（带误差学习）问题的难度。其次，我们构建了一种单轮协议，用于在$XY$平面上盲远程制备任意态直至Pauli-$Z$修正。