There exist infinitely many kinds of partial separability/entanglement

In tri-partite systems, there are three basic biseparability, A- BC, B- CA, and C- AB, according to bipartitions of local systems. We begin with convex sets consisting these biseparable states in the three-qubit system, consider arbitrary iterations intersections and/or hulls them get cones. One natural way classify is those which they belong or do not belong. This especially useful partial entanglement mixed states. show that lattice generated by respect hull intersection has infinitely many mutually distinct members see kinds entanglement. To this, we an increasing chain exhibit Greenberger–Horne–Zeilinger diagonal distinguishing chain.