Every PPT channel has finite entanglement-breaking index
Statement
We prove that every PPT linear map has finite entanglement-breaking index, thereby establishing the eventual entanglement-breaking property of PPT channels in full generality. Furthermore, by utilizing completely positive maps with low entanglement dimensionality, we show that a large family of PPT maps, which strictly containing the class of 2-superpositive maps, has entanglement-breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide strong evidence that the PPT-cubed conjecture may hold in full generality.
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No person has examined this. Nothing here has been checked at all. say whether it holds →
proof attempt · #1
Sang-Jun Park, using ChatGPT-5.6 SolThat credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.
The author states that AI tools including ChatGPT were used for exploratory mathematical discussions during development of the manuscript, in addition to language and LaTeX assistance. In particular, some ideas used in the proof-development process in Section 3 arose during interactions with GPT-5.6 Sol. These suggestions were subsequently examined, reformulated, incorporated into the manuscript, and independently verified by the author.
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