Lattice-Based Quantum Advantage from Rotated Measurements

• URL: http://arxiv.org/abs/2210.10143v3
• Date: Tue, 2 Jul 2024 16:29:20 GMT
• Title: Lattice-Based Quantum Advantage from Rotated Measurements
• Authors: Yusuf Alnawakhtha, Atul Mantri, Carl A. Miller, Daochen Wang,
• Abstract summary: We show a new technique that uses the entire range of qubit measurements from the $XY$-plane. We construct a one-round protocol for blind remote preparation of an arbitrary state on the $XY$-plane up to a Pauli-$Z$ correction.
• Score: 2.0249250133493195
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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