{"slug": "five-results-on-open-quantum-problems", "title": "Five Results on Open Quantum Problems", "summary": "PSI researchers working with an AI research system reported new results on five open problems in quantum information theory, each released with a paper, a Lean formalization and verification code in a public repository (oqp-batch-2026). The results include a proof that no choice of local observables violates the CHSH inequalities beyond a finite separation for two fixed-shape bounded regions in the vacuum of a massive free scalar field in 3+1 dimensions, and a proof that any PPT maps on a d-dimensional system suffice to break entanglement, improving on a recent OpenAI preprint showing two do not suffice in general. The team also proved Fourier-phase measurement strategies are optimal for producing CGLMP Bell violations and constructed a bipartite counterexample showing some extensibly causal processes admit no description as a larger finite-dimensional reversible process.", "body_md": "# Five results on Open Quantum Problems\n\nWorking with our AI research system, PSI researchers have obtained new results on five open problems in quantum information theory. Each result comes with a paper, a Lean formalization, and verification code, and the [release repository](https://github.com/physical-superintelligence/oqp-batch-2026) documents how AI was used in each.\n\n## OQP 2: Can states with a negative partial transpose have entanglement that cannot be distilled from any number of copies?\n\nWe study Werner states with a two-subsystem density matrix proportional to , where  exchanges the two subsystems. For every local dimension , Bell pairs cannot be distilled from three copies of these states when  (0.4625). Earlier published certificates establish the three-copy threshold  in dimensions [three](https://doi.org/10.5281/zenodo.23134454) and [four](https://github.com/GLiuax/d4-three-copy-werner). The question for arbitrarily many copies remains open.\n\n## OQP 12: Can vacuum correlations violate the CHSH Bell inequality at arbitrarily large separations?\n\nFor two fixed-shape bounded regions in the vacuum of a massive free scalar field in 3+1 dimensions, we prove that no choice of local observables violates the CHSH inequalities beyond a finite separation between the regions, even though the two regions remain entangled at arbitrary separation.\n\n## OQP 27: Which -outcome projective measurements on a fixed maximally entangled state of local dimension produce the largest CGLMP Bell violation?\n\nWe prove that Fourier-phase measurement strategies are optimal for producing Bell inequality violations, and we characterize every maximally Bell-violating measurement strategy as unitarily equivalent to such Fourier-phase measurements.\n\n## OQP 38: How many positive-partial-transpose (PPT) maps suffice to break entanglement?\n\nTwo do not suffice in general, as reported in a [recent OpenAI preprint](https://github.com/openai/math/blob/main/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf). We prove that any  PPT maps on a -dimensional system, , suffice. The maps can differ at each step, and their composition breaks entanglement with any reference system.\n\n## OQP 43: Can every process whose correlations remain causal, even with shared entangled ancillas, arise from a larger finite-dimensional reversible process?\n\nWe construct a bipartite counterexample to this claim. Namely, we show that there exist (extensibly) causal processes that admit no description in terms of a larger finite-dimensional reversible process.", "url": "https://wpnews.pro/news/five-results-on-open-quantum-problems", "canonical_source": "https://psi.inc/research/oqp-batch-2026/", "published_at": "2026-10-27 01:56:56+00:00", "updated_at": "2026-10-27 02:11:24.277756+00:00", "lang": "en", "topics": ["artificial-intelligence", "ai-research", "machine-learning"], "entities": ["PSI", "OpenAI", "Lean", "CHSH Bell inequality", "CGLMP Bell violation", "Werner states"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/five-results-on-open-quantum-problems", "markdown": "https://wpnews.pro/news/five-results-on-open-quantum-problems.md", "text": "https://wpnews.pro/news/five-results-on-open-quantum-problems.txt", "jsonld": "https://wpnews.pro/news/five-results-on-open-quantum-problems.jsonld"}}