Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 272-01. Entanglement with zero distillable secret key in local dimension ten
Manuscript map · lines 7935–7944
OpenAI@2026-10-07#rem:oai-p-272-01
Authors: OpenAI. Family 272.
Title: Entanglement with zero distillable secret key in local dimension ten.
Abstract: We construct an entangled state on ${}mathbb C{}{10}{}otimes{}mathbb C{}{10}$ 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 $M_{21}({}mathbb C)$ has a square that is not entanglement breaking.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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