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Keeping in view the exchange symmetry aspects in studies on spin squeezing ofmultiqubit states, we show that Ising type Hamiltonian does not retain theexchange symmetry of initially symmetric multiqubit states. Specifically, weshow that all N-qubit states (N greater than or equal to 5) obeying permutationsymmetry lose their symmetry after evolution with one dimensional Ising chainwith nearest neighbor interactions. Among 4-qubit symmetric pure states, only Wtype states retain their symmetry under time evolution with Ising Hamiltonian.

Loss of exchange symmetry in multiqubit states under Ising chain evolution