On the Limits of Stretching Quantum Pseudorandomness

2026-06-23

AI Summary

This work investigates whether quantum pseudorandom states (QPRS) possess output-stretching capabilities analogous to classical pseudorandom generators. By constructing a quantum oracle and analyzing security in the single-copy setting, the authors establish the first black-box separation between QPRS of different output lengths: they prove that QPRS with output length 1.1n exist, whereas those with length Ω(n^{2+ε}) cannot. Building upon the Common Haar Random State (CHRS) model and combining information-theoretic arguments with oracle construction techniques, the study introduces a novel method to bound the number of effectively usable resource states accessible to any generator. This yields a fundamental theoretical upper limit on QPRS output length, revealing an intrinsic constraint on their stretching capability.

Abstract

Pseudorandom states, introduced by Ji, Liu, and Song (CRYPTO '18), are quantum analogues of classical pseudorandom generators. A fundamental property of classical pseudorandom generators is that their output can be stretched to arbitrary polynomial length. Whether an analogous stretching property holds for quantum pseudorandom states remains unclear. In this work, we prove the first black-box separation between single-copy secure pseudorandom states ($\mathsf{1PRS}$) with different output lengths. Specifically, we construct a quantum oracle relative to which $\mathsf{1PRS}$ with output length $m(n)=1.1n$ exist, but $\mathsf{1PRS}$ with output length $m(n)=Ω(n^{2+ε})$ do not, for any $ε>0$. Our proof leverages the Common Haar Random State (CHRS) model introduced by Chen, Coladangelo, and Sattath (EUROCRYPT '25), and introduces a technique to bound the effective number of resource CHRS states utilized by any $\mathsf{1PRS}$ generator in this model.

Problem

• quantum pseudorandomness
• stretching
• pseudorandom states
• output length
• black-box separation

Innovation

• quantum pseudorandom states
• black-box separation
• output stretching
• CHRS model
• single-copy security