Constructing unextendible product bases from multiqubit ones

TL;DR

This paper presents methods to construct multipartite unextendible product bases (UPBs) from existing multiqubit UPBs, leading to new entangled states and insights into their entanglement properties.

Contribution

It introduces two new families of UPBs in multipartite systems derived from known multiqubit UPBs, expanding the tools for quantum entanglement research.

Findings

Constructed two families of UPBs in 2x2x4 and 2x2x2x4 systems.

Generated novel multipartite PPT entangled states.

Analyzed entanglement properties using geometric measure.

Abstract

The construction of multipartite unextendible product bases (UPBs) is a basic problem in quantum information. We respectively construct two families of $2\times2\times4$ and $2\times2\times2\times4$ UPBs of size eight by using the existing four-qubit and five-qubit UPBs. As an application, we construct novel families of multipartite positive-partial-transpose entangled states, as well as their entanglement properties in terms of the geometric measure of entanglement.