Five results on Open Quantum Problems

PSI Research

Five results on Open Quantum Problems

October 23, 2026

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 $I - α F$ , where $F$ exchanges the two subsystems. For every local dimension $d \geq 3$ , Bell pairs cannot be distilled from three copies of these states when $1 / d < α \leq 37 / 80$ (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.

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, $d \geq 2$ , 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.

Paper and proofs

← All research

OQP 2: Can states with a negative partial transpose have entanglement that cannot be distilled from any number of copies?

OQP 12: Can vacuum correlations violate the CHSH Bell inequality at arbitrarily large separations?

OQP 27: Which d-outcome projective measurements on a fixed maximally entangled state of local dimension d produce the largest CGLMP Bell violation?

OQP 38: How many positive-partial-transpose (PPT) maps suffice to break entanglement?

OQP 43: Can every process whose correlations remain causal, even with shared entangled ancillas, arise from a larger finite-dimensional reversible process?

OQP 27: Which $d$ -outcome projective measurements on a fixed maximally entangled state of local dimension $d$ produce the largest CGLMP Bell violation?