The unextendible product bases of four qubits: Hasse diagrams

We consider the unextendible product bases (UPBs) of fixed cardinality m in quantum systems of n qubits. These UPBs are divided into finitely many equivalence classes with respect to an equivalence relation introduced by N. Johnston. There is a natural partial order “≤ ” on the set of these equivalence classes for fixed m, and we use this partial order to study the topological closure of an equivalence class of UPBs. In the case of four qubits, for m= 8 , 9 , 10 , we construct explicitly the Hasse diagram of this partial order.