Necessity of nonmaximal entanglement for perfect nonlocal-game strategies
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Can a bipartite nonlocal game have a perfect finite-dimensional quantum strategy while every perfect strategy requires a nonmaximally entangled state? The issue is whether a maximally entangled state can always suffice.
Why it matters and what counts as progress
Why it matters: Such a game separates possession of entanglement from the particular entanglement spectrum needed for perfect play.
What counts as progress: An explicit finite game with a perfect nonmaximally entangled strategy and a proof excluding all perfect maximally entangled strategies.
How the problem developed
- 23 Jun 2015 · Question [1]
Laura Mančinska Studied whether bipartite pseudo-telepathy games can require perfect strategies that do not use maximally entangled states.
- 5 Aug 2026 · Counterexample [2]
Olivier Lalonde; the paper says AI tools played a decisive role in matrix search, pruning and certificate development, without naming a specific model Gave a bipartite game with input-set sizes 4 and 3 and output-set sizes 6 and 6 that has a perfect entangled strategy but none using a maximally entangled state.
AI contribution
Maximally entangled states are not complete for pseudo-telepathy
Lalonde gives a bipartite inner-product game with four and three inputs and six outputs. It has a perfect strategy using a nonmaximally entangled state, but no perfect finite-dimensional strategy using a maximally entangled state.
Sources
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Publication dates and editorial changes.
Codex-found game needs nonmaximal entanglement for a perfect strategy