Generic Number-of-Copies Amplification for Pseudorandom States

2026-06-28

AI Summary

This work addresses the problem of generically amplifying quantum pseudorandom states (PRS) that are secure only against adversaries with a single copy (1-PRS) into states secure against adversaries possessing an arbitrary polynomial number \( t \) of copies (\( t \)-PRS). By conducting a refined analysis of the randomness inherent in the construction and integrating techniques from quantum extractors, we achieve this amplification without requiring any additional assumptions. Our approach overcomes prior limitations that restricted such amplification to settings with only a small number of ancillary qubits, thereby providing—for the first time—a universal and unconditional method for copy-number security amplification applicable to any 1-PRS. This significantly broadens both the applicability and the security guarantees of quantum 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.

Problem

• quantum pseudorandom states
• copy amplification
• t-PRS
• single-copy security
• quantum cryptography

Innovation

• quantum pseudorandom states
• copy amplification
• quantum extractors
• ancilla elimination
• t-PRS