Every PPT channel has finite entanglement-breaking index

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.

Source: arXiv:2608.13551v1 - http://arxiv.org/abs/2608.13551v1 PDF: https://arxiv.org/pdf/2608.13551v1 Original Link: http://arxiv.org/abs/2608.13551v1