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

2025-01-07

AI Summary

This work addresses the secure construction of one-time memories (OTMs). We propose the first quantum single-qubit OTM scheme based solely on stateless hardware. Our method encodes two classical bits into a single qubit using quantum random access codes (QRACs) and employs an optimized non-convex POVM measurement on a two-level system to implement a selective readout mechanism: the user can recover either bit with high probability, while the other bit is information-theoretically erased irreversibly. Key contributions include: (i) the first integration of QRACs with non-convex POVM optimization for OTM security proofs, eliminating reliance on stateful hardware or strong cryptographic assumptions; and (ii) a rigorous derivation of a polynomially bounded computational error upper bound under polynomially many classical queries, yielding a succinct and verifiable information-theoretic security guarantee.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Non-convex Optimization
• Constraint Satisfaction and Optimization: Satisfiability

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Quantum Random Access Codes
• One-Time Memories
• Information Security

Innovation

• Quantum Random Access Codes
• One-Time Memories
• Enhanced Information Security