Abstract
The 4-qubit unextendible product bases (UPBs) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. Based on this study we show that there is only one UPB of size 6 and six UPBs of size 9 in , three UPBs of size 9 in , and no UPB of size 7 in and . Furthermore we construct a new family of 4-qubit positive-partial-transpose (PPT) entangled states of rank seven, and show that they are also PPT entangled states in and , respectively. We analytically derive a geometric measure of a special PPT entangled states.
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