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

• URL: http://arxiv.org/abs/2212.02446v1
• Date: Mon, 5 Dec 2022 17:42:47 GMT
• Title: Construction of multipartite unextendible product bases and geometric measure of entanglement of positive-partial-transpose entangled states
• Authors: Yize Sun, Baoshan Wang, Shiru Li
• Abstract summary: We show that there exist two families UPBs in Hilbert space $mathbbC2otimesmathbbC2otimesmathbbC2otimesmathbbC2otimesmathbbC4$ by merging two different systems of an existing $7$-qubit UPB of size $11$. A new family of $7$-qubit positive-partial-transpose entangled states of rank $27-11$ is constructed.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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