Lattice-Based Quantum Advantage from Rotated Measurements

TL;DR

This paper introduces a new measurement technique in quantum cryptography using the full range of qubit measurements in the XY-plane, enabling optimized proofs of quantumness and a one-round protocol for blind remote state preparation.

Contribution

It presents a novel measurement approach in quantum cryptography and demonstrates its advantages in two key applications, improving security and protocol efficiency.

Findings

Enhanced proof of quantumness with security based on LWE hardness

One-round protocol for blind remote state preparation on the XY-plane

Utilization of full qubit measurement range improves cryptographic protocols

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.