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The quantum entanglement problem is a central problem in quantum physics.A geometric measure of the entanglement of a general m-partite state can be described as the minimum distance to the set of separable states.The optimality conditions for the square of this minimum distance form the quantum eigenvalue problem.The quantum eigenvalues are all real.The largest quantum eigenvalue,called the entanglement eigenvalue,is corresponding to the nearest separable state.The quantum eigenvalue problem has a close link with the Z-eigenvalue problem.