Computing geometric measure of entanglement for symmetric pure states via the Jacobian SDP relaxation technique

DOI10.1007/s40305-016-0135-1zbMath1371.65033OpenAlexW2522285031MaRDI QIDQ2014679

Meng-Shi Zhang, Guyan Ni, Bing Hua

Publication date: 25 August 2017

Published in: Journal of the Operations Research Society of China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40305-016-0135-1

zbMATH Keywords

numerical examplessymmetric tensorsquantum entanglementpolynomial optimizationsemidefinite programming (SDP)geometric measureunitary symmetric eigenvalue

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical mathematical programming methods (65K05) Semidefinite programming (90C22) Multilinear algebra, tensor calculus (15A69) Quantum coherence, entanglement, quantum correlations (81P40)

Related Items (5)

Low Rank Symmetric Tensor Approximations ⋮ Symmetric Tensor Nuclear Norms ⋮ Calculating entanglement eigenvalues for nonsymmetric quantum pure states based on the Jacobian semidefinite programming relaxation method ⋮ Iterative methods for computing U-eigenvalues of non-symmetric complex tensors with application in quantum entanglement ⋮ Pseudospectra localizations for generalized tensor eigenvalues to seek more positive definite tensors

Uses Software

• SeDuMi
• GloptiPoly

Cites Work

• Tensor Decompositions and Applications
• An unconstrained optimization approach for finding real eigenvalues of even order symmetric tensors
• Z-eigenvalue methods for a global polynomial optimization problem
• On motivating the Mitchell-Todd modification of Karmarkar's algorithm for LP problems with free variables
• An exact Jacobian SDP relaxation for polynomial optimization
• The hierarchy of local minimums in polynomial optimization
• Spherical optimization with complex variables for computing US-eigenpairs
• Eigenvalues of a real supersymmetric tensor
• On the best rank-1 approximation to higher-order symmetric tensors
• Global Optimization with Polynomials and the Problem of Moments
• Rank-One Approximation to High Order Tensors
• On the Best Rank-1 Approximation of Higher-Order Supersymmetric Tensors
• Geometric Measure of Entanglement and U-Eigenvalues of Tensors
• Finding the extreme Z-eigenvalues of tensors via a sequential semidefinite programming method
• Shifted Power Method for Computing Tensor Eigenpairs
• GloptiPoly 3: moments, optimization and semidefinite programming
• Using SeDuMi 1.02, A Matlab toolbox for optimization over symmetric cones
• On the Best Rank-1 and Rank-(R₁ ,R₂ ,. . .,R_N) Approximation of Higher-Order Tensors
• The Best Rank-1 Approximation of a Symmetric Tensor and Related Spherical Optimization Problems
• All Real Eigenvalues of Symmetric Tensors

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