A Goldreich-Levin reduction for two entangled parties

Goldreich-Levin reductions are ubiquitous in cryptography: they convert an algorithm capable of guessing <r, m> mod 2, for a hidden string m and a random challenge r, into one that is capable of extracting the entirety of m. Here, I will describe a Goldreich-Levin reduction for two entangled parties who are capable of simultaneously guessing <r, m> given identical challenges r. This unlocks an alternative, arguably more modular and natural, proof of the existence of unclonable encryption (which was recently established by Ananth and Sahai, and Ragavan). This is joint work with Qipeng Liu and Ziyi Xie, but the solution was kindly provided by AI.