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- W2897723172 abstract "The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $cH=bbC^2oxbbC^2oxbbC^4$, three UPBs of size $9$ in $cK=bbC^4oxbbC^4$, and no UPB of size $7$ in $cH$ and $cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $r$ of rank seven, and show that it is also a PPT entangled state in $cH$ and $cK$, respectively. We analytically derive the geometric measure of entanglement of a special $r$." @default.
- W2897723172 created "2018-10-26" @default.
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- W2897723172 date "2018-10-21" @default.
- W2897723172 modified "2023-09-23" @default.
- W2897723172 title "Constructing $2times2times4$ and $4times4$ unextendible product bases and positive-partial-transpose entangled states" @default.
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- W2897723172 doi "https://doi.org/10.48550/arxiv.1810.08932" @default.
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