Constructing 2×2×4 and 4×4 unextendible product bases and positive-partial-transpose entangled states

2018/10/21 by Lin Chen, Kai Wang, Chen, Lin +7
Computer Science · Physics and Astronomy · #Quantum Information and Cryptography #Quantum Computing Algorithms and Architecture #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.1810.08932

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=\bbC²\ox\bbC²\ox\bbC⁴, three UPBs of size 9 in \cK=\bbC⁴\ox\bbC⁴, 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.

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