Baptista et al.’s conjecture on full-rank projective self-testing
For every nonlocal game , if self-tests a strategy among strategies consisting of a pure state of full Schmidt rank and projective measurements, then self-tests the same strategy without imposing the full-Schmidt-rank or projectivity assumptions; equivalently, every optimal unrestricted strategy for is equivalent to the designated full-rank projective strategy under the usual self-testing equivalence.
References
Primary source
Additional references
Progress summary
A September 2026 preprint claims to disprove the conjecture by exhibiting a game that separates full-rank projective self-testing from assumption-free self-testing.
The conjecture asks whether full rank and projective measurements can guarantee self-testing without additional assumptions. Earlier work formulated the conjecture and established related separations, but did not settle this exact statement.
September 2026 separating game
A new construction claims a nonlocal game with full-rank projective self-testing but without assumption-free self-testing, and classifies its optimal correlations. If correct, this is a counterexample to the conjecture and shows that full rank and projectivity alone do not provide the desired principle. The construction is explicitly unrefereed.
Current status (as of September 2026): The conjecture is claimed refuted by an unrefereed arXiv construction, but the result remains unverified.
Sources
- arxiv.org
- arxiv.org
- arxiv.org
- researchgate.net
- ui.adsabs.harvard.edu
- webhomes.maths.ed.ac.uk
- math.stackexchange.com
- quantamagazine.org
- mathoverflow.net
- par.nsf.gov
- ar5iv.labs.arxiv.org
- arxiv.org
- arxiv.org
- arxiv.org
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- mathstodon.xyz
- www-cdn.anthropic.com
Solutions 0
No solutions have been posted yet.