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

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