Lattice-Based Quantum Advantage from Rotated Measurements

TitleLattice-Based Quantum Advantage from Rotated Measurements
Publication TypeJournal Article
Year of Publication2022
AuthorsAlnawakhtha, Y, Mantri, A, Miller, C, Wang, D
Date Published10/18/2022
KeywordsCryptography and Security (cs.CR), Emerging Technologies (cs.ET), FOS: Computer and information sciences, FOS: Physical sciences, Quantum Physics (quant-ph)

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.