Entangled States with Positive Partial Transpose in Any-Dimensional Quantum System

It is well known that the positive partial transpose (PPT) criterion for determining separability is an operational separability criterion. However, in a high-dimensional (>6) situation, this criterion is not
sufficient. How can we judge whether an entangled state in any high-dimensional quantum system is PPT or not? Here we propose a linear algebra method for checking the positivity of the partial transpose of a state and present a set of entangled mixed states with non-positive partial transpose.