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.

翻译：伪随机量子态（PRS）是可高效构造的状态，在计算上与Haar随机态不可区分，且近期已在密码学领域得到应用。我们探索了伪随机态的新定义、新性质及应用，并做出以下贡献：1. 新定义：我们研究了由Ananth、Qian和Yuen（CRYPTO'22）提出的类伪随机函数态（PRFS）生成器的变体，其伪随机性质在生成器可被自适应查询或叠加查询时仍然成立。我们证明了这些变体在后量子单向函数存在下的可行性。2. 经典通信：我们证明了输出长度为对数的PRS生成器可蕴含经典通信下的承诺与加密方案。此前基于PRS生成器构造此类方案需要量子通信。3. 简化证明：我们给出了Brakerski-Shmueli（TCC'19）结果的简化证明，即具有随机二进制相位的均匀叠加态的多项式数量副本与Haar随机态不可区分。4. 计算假设的必要性：我们还证明了输出长度关于密钥长度为对数或更长的安全PRS必然需要计算假设。