{"id":"openai-math/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten","pdf":"https://github.com/openai/math/blob/main/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Entanglement-with-zero-distillable-secret-key-in-local-dimension-ten-September-27-2026","tags":["quantum-information","entanglement","quantum-cryptography"],"score":0,"title":"Entanglement with zero distillable secret key in local dimension ten","domain":"Mathematical physics","family":"272","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MP","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Entanglement without distillable secret key"}