# Asymmetry of tensor product of asymmetric and invariant vectors arising from Schur-Weyl duality based on hypergeometric orthogonal polynomial

@inproceedings{Hayashi2021AsymmetryOT, title={Asymmetry of tensor product of asymmetric and invariant vectors arising from Schur-Weyl duality based on hypergeometric orthogonal polynomial}, author={Masahito Hayashi and Akihito Hora and Shintarou Yanagida}, year={2021} }

We introduce and study a certain discrete probability distribution $P_{n,m,k,l}$ having non-negative integer parameters $n,m,k,l$, motivated by the asymmetry problem in quantum information theory. Its analysis reveals the number of orthogonal vectors among permuted vectors of the tensor product of asymmetric and invariant vectors. The distribution is defined by irreducible decomposition of the tensor product $\Xi_{n,m|k,l}$ of a certain asymmetric state and the Dicke state in the $\operatorname…

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