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

Authors: Prabhanjan Ananth , UCSB Aditya Gulati , UCSB Luowen Qian , Boston University Henry Yuen , Columbia University Search ePrint Search Google Slides TCC 2022 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 and applications of pseudorandom states, and present the following contributions: - We study variants of pseudorandom \emph{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. - We show that PRS generators with logarithmic output length imply commitment and encryption schemes with \emph{classical communication}. Previous constructions of such schemes from PRS generators required quantum communication. - 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. - We also show that logarithmic output length is a sharp threshold where PRS generators start requiring computational assumptions.
BibTeX
@inproceedings{tcc-2022-32582,
title={Pseudorandom (Function-Like) Quantum State Generators: New Definitions and Applications},
publisher={Springer-Verlag},
author={Prabhanjan Ananth and Aditya Gulati and Luowen Qian and Henry Yuen},
year=2022
}