Maximally entangled states are not complete for pseudo-telepathy

Olivier Lalonde

Maximally entangled states are not complete for pseudo-telepathy

Quantum Physics 2026-08-05 v1

Authors: Olivier Lalonde

Abstract

One of the longstanding open problems in quantum nonlocality is to determine if maximally entangled states are complete for bipartite pseudo-telepathic games: namely, if every nonlocal game which admits a perfect entangled strategy admits such a strategy which uses a maximally entangled state. We exhibit a counterexample to this in the form of a bipartite nonlocal game with input sets of size 4 and 3 and output sets both of size 6. This game is part of a new class of nonlocal games, which we call inner product games, which could be of independent interest.

Keywords

maximally entangled states pseudo-telepathy nonlocal games inner product games quantum nonlocality perfect entangled strategy

Cite

@article{arxiv.2608.05378,
  title  = {Maximally entangled states are not complete for pseudo-telepathy},
  author = {Olivier Lalonde},
  journal= {arXiv preprint arXiv:2608.05378},
  year   = {2026}
}