Pseudorandom unitaries require imaginarity, establishing fundamental limits on property testing and quantum pseudorandomness.
A single Haar random quantum state can be used to construct single-copy pseudorandom states (1PRS), which are computationally indistinguishable from a Haar random state for a single copy. However, this single Haar random state is not sufficient to construct the stronger notion of (multi-copy) pseudorandom states (PRS).