["How do I show that a two-qubit state is an entangled state?"](https://quantumcomputing.stackexchange.com/questions/2263/) includes [an answer](https://quantumcomputing.stackexchange.com/a/2266/2645) which references the [Peres–Horodecki criterion](https://en.wikipedia.org/wiki/Peres%E2%80%93Horodecki_criterion). This works for $2\times 2$ and $2\times3$ dimensional cases; however, in higher dimensions, it is "inconclusive." It is suggested to supplement with more advanced tests, such as those based on [entanglement witness](https://en.wikipedia.org/wiki/Entanglement_witness). How would this be done? Are there alternative ways to go about this?