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PSI Publishes Five AI-Assisted Quantum-Information Results
Physical Superintelligence says its October 23, 2026, release presents five quantum-information results, each with a paper and Lean formalization. The results address Werner states, vacuum Bell correlations, CGLMP measurements, PPT maps and
Quantum.world Team · Written with AI · fact-checked ·
PSI’s 23 October batch packages five proofs
Physical Superintelligence (PSI) published five results on open problems in quantum information on October 23, pairing each paper with a Lean 4 formalization and supporting files. The problems range from how entanglement behaves in Werner states to whether certain causal quantum processes can be described by reversible dynamics. PSI says its researchers developed the mathematics in automated workflows with AI models, while AI agents wrote the formalizations under the company’s direction.
The release includes papers, formal statements and proof files in a public GitHub repository. The result guides name Ian MacCormack, Ning Bao and David Turturean among the paper authors, and state that the named researchers remain responsible for correctness. The disclosures list models from OpenAI and Anthropic, with the model mix varying among results.
Werner states meet a finite Bell-distance limit
On Open Quantum Problem 2, PSI reports a bound for Werner states: in every local dimension d ≥ 3, Bell pairs cannot be distilled from three copies when 1/d < α ≤ 37/80, or 0.4625. The result concerns three copies, not an arbitrary number; whether such states remain undistillable for any number of copies is still open. The paper also gives sharper three-copy results in dimensions three and four, according to its result guide.
Problem 12 addresses vacuum correlations in a massive free scalar field in 3+1 dimensions. For two fixed, bounded regions, the result says no choice of local observables can violate the CHSH inequality once the regions are separated beyond a finite distance—even though they remain entangled at arbitrary separation. The OQP 12 paper is by David Turturean.
Fourier-phase measurements and PPT-map bounds
Problem 27 concerns CGLMP Bell inequalities, which test correlations between measurements with multiple outcomes. PSI says Fourier-phase projective measurements attain the largest violation for a fixed maximally entangled state, and characterizes all maximizing strategies in the stated setting as equivalent to those measurements up to a common unitary. The result addresses projective measurements; its guide specifies two measurement settings and d outcomes.
For Problem 38, the team proves that any 2(d−1) positive-partial-transpose (PPT) maps on a d-dimensional system suffice to produce an entanglement-breaking composition, even when the maps differ at each step. The composition also breaks entanglement with any reference system. The bound is not a proof that two PPT maps always suffice—the two-map question is the open problem the result addresses. PSI’s guide states the theorem for maps on d × d complex matrices.
A bipartite process resists purification
Problem 43 asks whether every process whose correlations remain causal, including with shared entangled ancillary systems, can be represented through a larger finite-dimensional reversible process. PSI’s answer is no: its paper constructs a bipartite counterexample. The OQP 43 result guide describes it as an explicit four-qubit process that is extensibly causal but not purifiable.
The release packages these findings as preprints, not as results already established through peer review. Its formalizations make selected mathematical statements and proof developments available in Lean, while the individual guides specify what each formalization covers. For example, the Werner-state guide says its Lean development formalizes the qutrit case of stated theorems; the package should not be read as claiming that every step of all five papers has been machine-checked.