Every PPT channel has finite entanglement breaking index

Abstract: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 contains the class of 2-superpositive maps, has entanglement breaking index bounded above by 3, uniformly in the dimension. In particular, these results provide evidence that the PPT-cubed conjecture may hold in full generality.

Quantum Physics (quant-ph); Mathematical Physics (math-ph); Operator Algebras (math.OA)

arXiv:2608.13551 [quant-ph]

(or arXiv:2608.13551v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.13551 Focus to learn more arXiv-issued DOI via DataCite

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