Characterizing unextendible product bases in qutrit-ququad system

Abstract

Unextendible product bases (UPBs) play an important role in quantum information theory. However, very little is known about UPBs in Hilbert space of local dimension more than three. In this paper, we study the UPBs in qutrit-ququad system and find that there only exist six, seven and eight-state UPBs. We completely characterize the six-state and seven-state UPBs. For eight-state UPBs, seven classes of UPBs are found. As auxiliary results, we study the distinguishability of qutrit-ququad UPBs by separable measurements, and find that there exists a UPB that cannot be distinguished.