| Quantum entanglement is one of the features that distinguish quantum physics from classical physics.Quantum entangled states play a key role in quantum information processing,which is an essential resource in many quantum information processing processes.The construction of unextendible product bases and its related problems is an important topic in the study of quantum information theory,and the construction of unextendible product bases has been of great interest.In this paper,we first verify that when the unextendible product bases(UPBs)with sizes of 6,8,9,and 10 in the 5-qubit system are considered as product vectors in a coarsening system(i.e.,merging some subsystems,e.g.,merging two subsystems,the system becomes 2 ? 2 ? 2 ? 4),some of these product vectors are still unextendible product bases,and some are no longer unextendible product bases.For unextendible product bases that are no longer coarsening systems,we focus on how to make them expanded to unextendible product bases in the coarsened system by adding some product vectors.Secondly,we obtain UPBs with the same size from different unextendible product bases of 5-qubit and it is easy to verify that these unextendible product bases are inequivalent to each other.In addition,the unextendible product bases we obtained are not equivalent to the existing ones although the sizes are the same.We obtained new unextendible product bases by coarsening system from the5-qubit UPBs.In general,the constructing of unextendible product bases in the multipartite space with lower dimension of subsystems is easier than that of higher dimension.So we can construct unextendible product bases in system with lower dimensional subsystems at first,and then derive unextendible product bases with the higher one in terms of the coarsening structure of the system. |
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