The unextendible product bases of four qubits: Hasse diagrams

Abstract

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 `$\le$' 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.

31 pages, the appendix starts from p13

References in corpus (1)

• The Structure of Qubit Unextendible Product Bases

Cited by in corpus (1)

• Constructing $2\times 2\times 4$ and $4\times 4$ unextendible product bases and positive-partial-transpose entangled states