Generic Number-of-Copies Amplification for Pseudorandom States
This resolves a fundamental question in quantum cryptography, showing that single-copy security suffices for multi-copy security of pseudorandom states, which is important for cryptographic applications.
The authors prove that any 1-PRS (single-copy secure pseudorandom state) can be amplified to a t-PRS (t-copy secure) for any polynomial t, without additional assumptions, solving a problem left open by prior work that only handled restricted constructions.
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.