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.

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 $I-\alpha F$, where $F$ exchanges the two subsystems. For every local dimension $d\ge 3$, Bell pairs cannot be distilled from three copies of these states when $1/d<\alpha \le 37/80$ (0.4625). Earlier published certificates establish the three-copy threshold $\alpha =1/2$ 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 $d$-outcome projective measurements on a fixed maximally entangled state of local dimension $d$ 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 $2(d-1)$ PPT maps on a $d$-dimensional system, $d\ge 2$, 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.