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The geometric measure of entanglement is a widely used entanglement measurefor quantum pure states. The key problem of computation of the geometricmeasure is to calculate the entanglement eigenvalue, which is equivalent tocomputing the largest unitary eigenvalue of a corresponding complex tensor. Inthis paper, we propose a Jacobian semidefinite programming relaxation method tocalculate the largest unitary eigenvalue of a complex tensor. For this, wefirst introduce the Jacobian semidefinite programming relaxation method for apolynomial optimization with equality constraint, and then convert the problemof computing the largest unitary eigenvalue to a real equality constrainedpolynomial optimization problem, which can be solved by the Jacobiansemidefinite programming relaxation method. Numerical examples are presented toshow the availability of this approach.

Calculating Entanglement Eigenvalues for Non-Symmetric Quantum Pure States Based on the Jacobian Semidefinite Programming Relaxation Method