Generic Number-of-Copies Amplification for Pseudorandom States

Abstract: We show that any quantum pseudorandom state that is secure against single-copy distinguishers, i.e. a $1$-PRS, can be amplified to $t$-copy security, i.e. to a $t$-PRS, without additional assumptions, for any polynomial $t$ in the security parameter. Prior work (Ananth and Goldin, arXiv 2025) was only able to show this for a restricted class of $1$-PRS constructions, namely ones whose generators only use a small number of ancilla qubits. Technically, we show that by carefully accounting for the randomness that is used in the construction, and using quantum extractors, it is possible to eliminate an ancilla register of any length and obtain a meaningful $t$-PRS outcome.