Mathematical physics·OpenAI Math·Result 272·Lean formalisation listed
Entanglement without distillable secret key
One of the 372 results in OpenAI's public mathematics catalogue, filed under mathematical physics: 1 preprint, the latest dated 27 September 2026. This page quotes OpenAI's own summary of the claim, links the paper and abstract, and will embed the animation.
Latest paper
Entanglement with zero distillable secret key in local dimension ten
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What OpenAI claims
Constructs an entangled state on ℂ10⊗ℂ10 with zero distillable secret key for the specified local-instrument protocols that complete almost surely. These allow joint local processing and authenticated two-way public communication, with no other shared private resource and an eavesdropper holding the input purification and public record. A trace-preserving PPT channel on M21(ℂ) whose square is not entanglement breaking disproves Christandl's PPT-square conjecture. (Lean)
Paper
Entanglement with zero distillable secret key in local dimension ten
We construct an entangled state on ℂ10⊗ℂ10 with zero distillable secret key for the local-instrument protocols specified here. They allow joint processing of all copies and unlimited two-way public communication, with the input as the only shared private resource and an eavesdropper holding a purification and the complete public record. The construction also disproves the unrestricted two-map PPT-composition conjecture. A separate trace-preserving PPT channel on M21(ℂ) has a square that is not entanglement breaking.
Status
Preprint. The paper has not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.
