Quantum One-Time Memories from Stateless Hardware, Random Access Codes, and Simple Nonconvex Optimization

TL;DR

This paper introduces a quantum-based construction of one-time memories using stateless hardware and quantum random access codes, providing bounds on security through nonconvex optimization.

Contribution

It presents a novel quantum encoding scheme for OTMs with security proofs based on nonconvex optimization over quantum measurements.

Findings

Quantum encoding of two bits into a single qubit with probabilistic retrieval

Upper bounds on the probability of distinguishing bits based on optimization

Soundness proof against polynomial classical queries to hardware

Abstract

We present a construction of one-time memories (OTMs) using classical-accessible stateless hardware, building upon the work of Broadbent et al. and Behera et al.. Unlike the aforementioned work, our approach leverages quantum random access codes (QRACs) to encode two classical bits, $b_0$ and $b_1$, into a single qubit state $\mathcal{E}(b_0 b_1)$ where the receiver can retrieve one of the bits with a certain probability of error. To prove soundness, we define a nonconvex optimization problem over POVMs on $\mathbb{C}^2$. This optimization gives an upper bound on the probability of distinguishing bit $b_{1-\alpha}$ given that the probability that the receiver recovers bit $b_\alpha$ is high. Assuming the optimization is sufficiently accurate, we then prove soundness against a polynomial number of classical queries to the hardware.