Entanglement of quantum states is one of the most fundamental and essential notions in quantum information theory, because of its usefulness in many kinds of quantum protocols and computations. However, studying entanglement is in general difficult, both from mathematical and computational points of view. In this talk, we propose a method that can be efficient to characterize the entanglement of quantum states having some symmetry called invariance. We apply the characterization to discuss PPT entanglement for various invariant quantum states including well-known examples such as bipartite or tripartite Werner states and new examples such as the standard permutation symmetry.
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