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Characterizing unextendible product bases in qutrit-ququad system
Ying-Hui Yang1, Fei Gao2, Guang-Bao Xu2
11] State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China [2] School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, 454000, China.
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.
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