Scalable, Quantum-Accessible, and Adaptive Pseudorandom Quantum State and Pseudorandom Function-Like Quantum State Generators

Jul 16, 2026

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New constructions for pseudorandom quantum states (PRS) and pseudorandom function-like quantum state (PRFS) generators achieve three targeted properties: scalability, quantum accessibility, and adaptivity. Scalability allows security parameters to exceed the number of qubits; quantum accessibility permits adversaries to supply quantum inputs; adaptivity allows queries in an online, adaptive manner. An isometric preparation procedure yields states arbitrarily close to Haar randomness in the true-random setting and negligible distinguishing advantage in the pseudorandom setting, giving scalable, quantum-accessible, and adaptive PRFS under quantum-secure one-way functions.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages52

Reading Time2 h 11 min

Introduction

Technical overview

Random amplitudes quantum state

(Pseudo)random quantum state

(Pseudo)random function-like quantum state generator

Preliminaries

Notations

Probability distributions

Quantum cryptography

Isometric asymptotically random state generator

Random amplitudes procedure

Random phases procedure

Asymptotically random states

Pseudorandom quantum state generators

(Pseudo)random function-like quantum state generators

arXiv :2507 .22535v5 [ quant-ph] 13 Jul 2026 Scalable, quantum-accessible, and adaptive pseudorandom quantum state and pseudorandom function-like quantum state generators Rishabh Batra 1 [0000-0002-5829-2304], Zhili Chen1 [0009-0002-2155-5817], Rahul Jain 1 ,2 ,3 [0000-0002-3649-6576], and YaoNan Zhang1 [0009-0009-3760-9729] 1 Centre for Quantum Technologies, Singapore {rishabhbatra,chen.zhili,[zhang.yaonan}@u.nus.edu](zhang.yaonan}@u.nus.edu) 2 Department of Computer Science, National University of Singapore [rahul@comp.nus.edu.sg](rahul@comp.nus.edu.sg) 3 MajuLab, UMI 3654, Singapore Abstract. We show new constructions for pseudorandom quantum states (PRS) and pseudorandom function-like quantum state (PRFS) generators satisfying scalability, which means the security parameter can be much larger than the number of qubits, quantum accessibility, which means the adversary can provide quantum input, and adaptivity, which means the adversary can query it adaptively. We present an isometric procedure to prepare quantum states that can be arbitrarily random (i.e., the trace distance from the Haar-random state can be arbitrarily small for the true random case, or the distinguishing advantage can be arbitrarily small for the pseudorandom case) . This naturally gives the first construction for scalable, quantum-accessible, and adaptive PRFS assuming quantum-secure oneway functions. Compared to prior PRFS works, we use a stronger definition of quantum accessibility in which the adversary can be ancilla-assisted, i.e., the input state may not be pure and could be entangled with other quantum registers. Thus, our result also gives the first (fully) quantum-accessible PRFS. Our PRFS construction implies various primitives, including long-input PRFS, short-input PRFS, short-output PRFS, non-adaptive PRFS, and classically-accessible adaptive PRFS [AQY22,AGQY22] . This new construction may be helpful in simplifying the microcrypt zoo. Keywords: Quantum cryptography · Pseudorandom quantum state. 1 Introduction ........................................................................... 2 2 Technical overview ..................................................................... 7 2.1 Random amplitudes quantum state .................................................. 7 2.2 (Pseudo)random quantum state ..................................................... 8 2.3 (Pseudo)random function-like quantum state generator ................................. 9 3 Preliminaries .......................................................................... 10 3.1 Notations ........................................................................ 10 3.2 Probability distributions ........................................................... 11 3.3 Quantum cryptography ............................................................ 12 4 Isometric asymptotically random state generator ........................................... 15 4.1 Random amplitudes procedure ...................................................... 16 4.2 Random phases procedure .......................................................... 17 4.3 Asymptotically random states ....................................................... 18 5 Pseudorandom quantum state generators .................................................. 19 6 (Pseudo)random function-like quantum state generators .................................... 20 A Alternative proof of ARS ............................................................... 28 B Proof of asymptotically random to pseudorandom .......................................... 32 C Proof of the random amplitudes quantum state from Beta variables .......................... 33 D Proof of that random phase gives standard Gaussian ....................................... 34 E Proof of upper bound of diamond norm distance ........................................... 34 F Proof of claim about the scalable pseudorandom state gen

FAQs

What three properties do the proposed PRS/PRFS generators satisfy?

They satisfy scalability (security parameter can exceed qubit count), quantum accessibility (adversary can provide quantum input, including ancilla-assisted/entangled inputs), and adaptivity (adversary can query adaptively).

How are the pseudorandom (and true-random) quantum states prepared?

An isometric procedure prepares states that can be made arbitrarily random, yielding arbitrarily small trace distance from the Haar-random state in the true-random case and arbitrarily small distinguishing advantage in the pseudorandom case.

What kinds of PRFS primitives are implied by the construction?

The construction implies multiple PRFS variants, including long-input, short-input, short-output, non-adaptive, and classically-accessible adaptive PRFS.

Jul 16, 2026

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