Need for Coherent Access in Constructing Quantum Cryptography

2026-09-30

AI Summary

This study addresses the unclear dependence of pseudorandom state constructions on access models in quantum cryptography. Leveraging quantum computational complexity theory and oracle separation techniques, this work rigorously distinguishes between classical and coherent access models for the first time. Specifically, it constructs an oracle world in which quantum-secure one-way functions exist yet long-output pseudorandom states do not. These results reveal the inherent limitations of classical access and demonstrate that length extension for pseudorandom states necessarily relies on coherent access. By establishing theoretical boundaries for such constructions, this research provides crucial theoretical support for understanding the role of access privileges in quantum black-box computation.

Abstract

We construct quantum oracles relative to which quantum-secure one-way functions (OWFs) exist but pseudorandom states (PRSs) with superlogarithmic output length do not. At first glance, this appears to contradict the known black-box constructions of PRS generators from quantum-secure OWFs. The distinction lies in the access model to the oracles; our oracle separation uses \emph{classical-accessible} random oracles that can be accessed only classically even by quantum algorithms. In fact, our impossibility of PRSs applies to \emph{any} classically accessible classical oracle in place of the random oracle, while keeping the other oracle component unchanged, showing the need for coherent access in constructing PRSs. We further show that logarithmic output length pseudorandom function-like states (PRFSs) exist relative to our oracles, giving an oracle separation between classically accessible logarithmic length PRFSs and superlogarithmic length PRSs. This shows that fully black-box PRS length extension from logarithmic to superlogarithmic output length must use coherent access to the underlying short PRS.

Problem

• quantum cryptography
• pseudorandom states
• coherent access
• oracle separation
• one-way functions

Innovation

• quantum oracles
• pseudorandom states
• coherent access
• classical-accessible random oracles
• oracle separation