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

Constructs an entangled state on ${\mathbb{C}}^{10}\otimes {\mathbb{C}}^{10}$ 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 $M_{21}(\mathbb{C})$ whose square is not entanglement breaking disproves Christandl s PPT-square conjecture.

The authors are OpenAI. This companion does not verify the proof. The claim is not a theorem of the Enter series and not a premise of any registered sheet. It does not close O.1. O.1 stays NOT_CLOSED. It is not a de Sitter state and not the QdS external-leg scheme. No quantum coefficient is admitted. No compilation is asserted.