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：陷门无爪函数（TCFs）在经典客户端与量子服务器之间的密码学交互中具有重要价值。典型协议要求量子服务器制备一对爪中两个比特串的叠加态，随后使用Pauli-$X$或$Z$测量对其进行测量。本文提出一种新技术，利用$XY$平面上的完整量子比特测量范围。我们在两个应用中展示了该方法的优势：首先，基于（Brakerski等人2018，Kalai等人2022）的研究，我们提出一种优化的两轮量子性证明方案，其安全性可直接表述为LWE（带误差学习）问题的困难性；其次，我们构建了单轮协议，可在至多Pauli-$Z$修正的精度下，盲态远程制备$XY$平面上的任意量子态。