# Five Results on Open Quantum Problems

> Source: <https://psi.inc/research/oqp-batch-2026/>
> Published: 2026-10-27 01:56:56+00:00

# 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.