Five Results on Open Quantum Problems

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.

Five results on Open Quantum Problems Working 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. OQP 2: Can states with a negative partial transpose have entanglement that cannot be distilled from any number of copies? We 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. OQP 12: Can vacuum correlations violate the CHSH Bell inequality at arbitrarily large separations? For 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. OQP 27: Which -outcome projective measurements on a fixed maximally entangled state of local dimension produce the largest CGLMP Bell violation? We 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. OQP 38: How many positive-partial-transpose PPT maps suffice to break entanglement? Two 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. OQP 43: Can every process whose correlations remain causal, even with shared entangled ancillas, arise from a larger finite-dimensional reversible process? We 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.