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OpenAI · 272-01 · 2026-09-27 · Mathematical physics

Entanglement with zero distillable secret key in local dimension ten

preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026

Family 272. Entanglement without secret key and the PPT-square conjecture.

The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.

Read against the standing problems

Tests. An entanglement statement is not gravity-generated entanglement and not an experimental exclusion of classical gravity. Oai272-A records a conditional bit-gap and does not verify Family 272. Oai276-A records a conditional one-use audit and does not verify 276-01. A non-entanglement-breaking channel is not gravity-generated entanglement. Oai279-A's finite factoring circuit is not gravity-generated entanglement and does not verify 279-01. Oai227-A's finite SK certificate is not gravity-generated entanglement and does not verify 227-01. Oai119-A's finite Hellinger certificate is not gravity-generated entanglement and does not verify 119-01. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. Oai119-A · Oai227-A · Oai279-A · Oai276-A · Oai272-A · En02-A · En01-C · Hawk03-A

Constructs an entangled state on 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 whose square is not entanglement breaking disproves Christandl s PPT-square conjecture.

We construct an entangled state on 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 has a square that is not entanglement breaking.

Preprint source and Lean scope

The abstract above is the catalogue abstract. The sections below are the full preprint source, 0 sections. This page is not only the abstract. The manuscript file is loading.

This preprint is named in the Lean scope note for 272: Entanglement without distillable secret key. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.

DimensionTenChannel.lean · DimensionTenChannel.lean

Statement file

DimensionTenPair.lean · DimensionTenPair.lean
Statement file
  • Tests
    External entanglement is not gravity-generated
    Family 272 records an entangled state with no distillable secret key under a stated protocol. That state is not gravity-generated entanglement and not an experimental exclusion of classical gravity. Oai272-A records a conditional local audit and does not verify 272-01. The authors of the external preprint are OpenAI. The companion does not verify those proofs.
    TestsOai272-A conditional bit-gapEn02-A capacity ledgerHawk03-A encoded partner