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 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 and four. 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. 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.