Two recent papers of Jun-Li Li and Cong-Feng Qiao (arXiv:1607.03364 and arXiv:1708.05336) present "practical schemes for the decomposition of a bipartite mixed state into a sum of direct products of local density matrices".

I would like to know if this methodology can be applied to (two-qubit, qubit-qutrit, two-qutrit,...) $X$-states (only the diagonal and antidiagonal entries of the corresponding density matrices being non-zero).

If this can be successfully accomplished, it might be useful in addressing the question of what amount, if any, does the two-retrit $X$-state Hilbert-Schmidt PPT-probability of $\frac{16}{3 \pi^2} \approx 0.54038$ correspond to bound entangled states--an issue I have raised in my earlier postings (Are X-state separability and PPT- probabilities the same for the two-qubit, qubit-qutrit, two-qutrit, etc. states? and What proportions of certain sets of PPT-two-retrit states are bound entangled or separable?)



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