2018
DOI: 10.48550/arxiv.1810.08932
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Constructing $2\times2\times4$ and $4\times4$ unextendible product bases and positive-partial-transpose entangled states

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 H = C 2 ⊗ C 2 ⊗ C 4 , three UPBs of size 9 in K = C 4 ⊗ C 4 , and no UPB of size 7 in H and K. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state ρ of rank seven, and show that it is also a PPT entangled state in H and K, respectively. We analytically derive the g… Show more

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“…In this paper we show that there are six 4 × 4 UPBs of size eight consisting of 4-qubit product vectors. It turns out to be much harder than the construction of 4 × 4 UPBs of size 6, 7 and 9 consisting of 4-qubit product vectors [26]. We do not rely on the classification of 4-qubit UPBs by programming in [11].…”
Section: Introductionmentioning
confidence: 99%
“…In this paper we show that there are six 4 × 4 UPBs of size eight consisting of 4-qubit product vectors. It turns out to be much harder than the construction of 4 × 4 UPBs of size 6, 7 and 9 consisting of 4-qubit product vectors [26]. We do not rely on the classification of 4-qubit UPBs by programming in [11].…”
Section: Introductionmentioning
confidence: 99%