Quantum One-Time Memories from Stateless Hardware, Random Access Codes, and Simple Nonconvex Optimization
Lev Stambler
TL;DR
The paper shows how to construct one-time memories from stateless hardware by encoding two classical bits into a single qubit via quantum random access codes (QRACs). A simple nonconvex POVM optimization on $2$-dimensional states bounds the cryptographic disturbance after measurement, enabling a soundness proof against polynomially many classical hardware queries under a conjectured bound. The protocol samples random strings and uses $n$ QRAC states to encode them, requiring recovery of a fraction of the chosen string to unlock the corresponding message, with correctness guaranteed by the QRAC success probability $\\cos^2(\pi/8)\approx 0.854$ and Chernoff-type concentration; security follows from a hybrid-based simulator argument and a fuzzy-lock/VBB-like obfuscation of the classical queries to stateless hardware. This work demonstrates a pathway to OTMs with classical-accessible hardware leveraging quantum encoding, and highlights a potential separation between classical and quantum oracle access in cryptographic primitives.
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 $b_{1-α}$ given that the probability that the receiver recovers bit $b_α$ is high. Assuming the optimization is sufficiently accurate, we then prove soundness against a polynomial number of classical queries to the hardware.