Geometric measure of entanglement of symmetric d-qubits is polynomial-time computable

2016/08/03 by Shmuel Friedland, Li Wang, Friedland, Shmuel +1 · 1 citation
Mathematics · Physics and Astronomy · #13P15 #15A69 #65H04 #81P40 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Rings and Algebras (math.RA) #math-ph #math.MP #math.RA #msc:13P15 #msc:15A69 #msc:65H04 #msc:81P40 #quant-ph

paper · pdf · doi:10.48550/arxiv.1608.01354

revised version, 36 pages, 18 tables

arxiv created 2017/03/06 · arxiv updated 2017/03/07

Abstract

We give a simple formula for finding the spectral norm of d-mode symmetric tensor in two variables over the complex or real numbers in terms of the complex or real roots of a corresponding polynomial in one complex variable. This result implies that the geometric measure of entanglement of symmetric d-qubits is polynomial-time computable. We discuss a generalization to d-mode symmetric tensor in more than two variables.

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• Spectral norm of a symmetric tensor and its computation

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