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arXiv:2212.02446

Construction of multipartite unextendible product bases and geometric measure of entanglement of positive-partial-transpose entangled states

Yize Sun, Baoshan Wang, Li, Shiru

Published Dec 5, 2022• 0 citations
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Abstract

In quantum information theory, it is a fundamental problem to construct multipartite unextendible product bases (UPBs). We show that there exist two families UPBs in Hilbert space $\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^2\otimes\mathbb{C}^4$ by merging two different systems of an existing $7$-qubit UPB of size $11$. Moreover, a new family of $7$-qubit positive-partial-transpose (PPT) entangled states of rank $2^7-11$ is constructed. We analytically derive a geometric measure of entanglement of a special PPT entangled states. Also an upper bound are given by two methods.

DOI
10.48550/arxiv.2212.02446

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