The proposed necessary and sufficient realignment criterion for X-states is conditional on the PPT criterion and therefore reproduces PPT rather than providing an independent test.
Gurvits, Classical deterministic complexity of edmonds’ problem and quantum entanglement (2003), arXiv:quant- ph/0303055 [quant-ph]
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Realignment Criterion: A necessary and sufficient condition for two-qubit $X$-states
The proposed necessary and sufficient realignment criterion for X-states is conditional on the PPT criterion and therefore reproduces PPT rather than providing an independent test.