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

2022/12/05 by Sun, Yize, Wang, Baoshan, Li, Shiru
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2212.02446

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 ℂ²⊗ℂ²⊗ℂ²⊗ℂ²⊗ℂ²⊗ℂ⁴ 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 2⁷-11 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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