Translating Between the Common Haar Random State Model and the Unitary Model

2025-03-14

AI Summary

A fundamental “model gap” persists between the CHRS model and the more stringent unitary model in quantum cryptography, rendering existing CHRS separations non-transferable to the unitary model without error. Method: We introduce the first universal uplift condition and establish a modular, verifiable transformation framework. Leveraging quantum query complexity analysis, explicit simulator construction, distributional equivalence proofs, and arguments based on Haar measure and unitary invariance, we systematically rectify critical flaws in prior work. Contribution/Results: Our framework simplifies and strengthens unitary-model separation proofs for foundational quantum cryptographic primitives—including the quantum random oracle and unclonable signatures—while, for the first time, lifting several CHRS-only separations to the full unitary model. This provides a unified, rigorous foundation for black-box separation theory in quantum cryptography.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Applications of cryptography
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Black-box separations are a cornerstone of cryptography, indicating barriers to various goals. A recent line of work has explored black-box separations for quantum cryptographic primitives. Namely, a number of separations are known in the Common Haar Random State (CHRS) model, though this model is not considered a complete separation, but rather a starting point. A few very recent works have attempted to lift these separations to a unitary separation, which are considered complete separations. Unfortunately, we find significant errors in some of these lifting results. We prove general conditions under which CHRS separations can be generically lifted, thereby giving simple, modular, and bug-free proofs of complete unitary separations between various quantum primitives. Our techniques allow for simpler proofs of existing separations as well as new separations that were previously only known in the CHRS model.

Problem

• Lifting CHRS separations to unitary separations
• Correcting errors in recent lifting results
• Providing modular proofs for quantum primitives separations

Innovation

• Lifts CHRS separations to unitary separations
• Provides modular, bug-free proofs
• Simplifies proofs of quantum separations