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 documents how AI was used in each.

We study Werner states with a two-subsystem density matrix proportional to I−αF, where F exchanges the two subsystems. For every local dimension d≥3, Bell pairs cannot be distilled from three copies of these states when 1/d<α≤37/80 (0.4625). Earlier published certificates establish the three-copy threshold α=1/2 in dimensions three and four. The question for arbitrarily many copies remains open.

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.

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.

Two do not suffice in general, as reported in a recent OpenAI preprint. We prove that any 2(d−1) PPT maps on a d-dimensional system, d≥2, suffice. The maps can differ at each step, and their composition breaks entanglement with any reference system.

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.