An introduction to recent work on analysis over the non-Archimedean Levi-Civita field related to applications for common numerical tasks is provided. After studying the algebraic, order, and topological properties, a calculus is developed under which central concepts like the intermediate value theorem, mean value theorem, and Taylor’s theorem with remainder hold under slightly stronger conditi...

We present a strong parallel repetition theorem for the entangled value of multi-player, oneround free games (games where the inputs come from a product distribution). Our result is the first parallel repetition theorem for entangled games involving more than two players. Furthermore, our theorem applies to games where the players are allowed to output (possibly entangled) quantum states as ans...