Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications

TL;DR

This paper introduces new definitions, properties, and applications of pseudorandom quantum states, demonstrating their cryptographic utility, feasibility under certain assumptions, and simplifying existing proofs in quantum information theory.

Contribution

It presents novel variants of pseudorandom function-like state generators, shows their cryptographic applications with classical communication, simplifies key existing proofs, and discusses the necessity of computational assumptions.

Findings

Variants of PRFS generators are feasible assuming post-quantum one-way functions.

PRS generators with logarithmic output length enable classical cryptographic schemes.

A simplified proof of indistinguishability of certain quantum states from Haar-random states.

Abstract

Pseudorandom quantum states (PRS) are efficiently constructible states that are computationally indistinguishable from being Haar-random, and have recently found cryptographic applications. We explore new definitions, new properties and applications of pseudorandom states, and present the following contributions: 1. New Definitions: We study variants of pseudorandom function-like state (PRFS) generators, introduced by Ananth, Qian, and Yuen (CRYPTO'22), where the pseudorandomness property holds even when the generator can be queried adaptively or in superposition. We show feasibility of these variants assuming the existence of post-quantum one-way functions. 2. Classical Communication: We show that PRS generators with logarithmic output length imply commitment and encryption schemes with classical communication. Previous constructions of such schemes from PRS generators required quantum communication. 3. Simplified Proof: We give a simpler proof of the Brakerski--Shmueli (TCC'19) result that polynomially-many copies of uniform superposition states with random binary phases are indistinguishable from Haar-random states. 4. Necessity of Computational Assumptions: We also show that a secure PRS with output length logarithmic, or larger, in the key length necessarily requires computational assumptions.