2012/03/16 by Shenglong Hu, Liqun Qi, Hu, Shenglong +3
Computer Science · Mathematics · Physics and Astronomy · #81Q99 #Black Holes and Theoretical Physics #FOS: Physical sciences #Matrix Theory and Algorithms #Quantum Physics (quant-ph) #Tensor decomposition and applications #msc:81Q99 #quant-ph
paper · pdf · doi:10.48550/arxiv.1203.3675
21 pages
openalex publication_date 2012/03/16 · arxiv created 2012/03/29 · arxiv updated 2015/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The geometric measure of entanglement for a symmetric pure state with nonnegative amplitudes has attracted much attention. On the other hand, the spectral theory of nonnegative tensors (hypermatrices) has been developed rapidly. In this paper, we show how the spectral theory of nonnegative tensors can be applied to the study of the geometric measure of entanglement for a pure state with nonnegative amplitudes. Especially, an elimination method for computing the geometric measure of entanglement for symmetric pure multipartite qubit or qutrit states with nonnegative amplitudes is given. For symmetric pure multipartite qudit states with nonnegative amplitudes, a numerical algorithm with randomization is presented and proven to be convergent. We show that for the geometric measure of entanglement for pure states with nonnegative amplitudes, the nonsymmetric ones can be converted to the symmetric ones.