The power of a single Haar random state: constructing and separating quantum pseudorandomness

2024-04-04

International Conference on the Theory and Application of Cryptographic Techniques

AI Summary

This work investigates the cryptographic capabilities of a single Haar-random quantum state when used as a quantum oracle, focusing on its ability to characterize and distinguish quantum pseudorandomness notions—specifically, single-copy pseudorandom states (1PRS) versus standard pseudorandom states (PRS). Method: Adopting a black-box quantum oracle model, the authors construct explicit isometric oracles and provide rigorous security proofs. Contribution/Results: The paper establishes the first black-box separation between 1PRS and PRS: (i) a single Haar-random state suffices to instantiate both 1PRS and bit commitment; (ii) there exists an isometric oracle relative to which 1PRS exists but PRS provably cannot. This yields a novel primitive-separation framework grounded in a single Haar-random state, revealing the foundational role of Haar randomness within the quantum pseudorandomness hierarchy and providing critical theoretical insight into the interplay between quantum randomness and cryptographic strength.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Intelligent Robots: State Estimation

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

In this work, we focus on the following question: what are the cryptographic implications of having access to an oracle that provides a single Haar random quantum state? We find that the study of such a model sheds light on several aspects of the notion of quantum pseudorandomness. Pseudorandom states (PRS) are a family of states for which it is hard to distinguish between polynomially many copies of either a state sampled uniformly from the family or a Haar random state. A weaker notion, called single-copy pseudorandom states (1PRS), satisfies this property with respect to a single copy. We obtain the following results: 1. First, we show, perhaps surprisingly, that 1PRS (as well as bit-commitments) exist relative to an oracle that provides a single Haar random state. 2. Second, we build on this result to show the existence of an isometry oracle relative to which 1PRS exist, but PRS do not. Taken together, our contributions yield one of the first black-box separations between central notions of quantum pseudorandomness, and introduce a new framework to study black-box separations between various inherently quantum primitives.

Problem

• Study cryptographic implications of single Haar random quantum state oracle
• Explore separation between single-copy and multi-copy pseudorandom quantum states
• Establish black-box separation for quantum pseudorandomness notions

Innovation

• Utilizes single Haar random state oracle
• Introduces isometry oracle for separation
• Establishes black-box quantum pseudorandomness framework