Loss of Exchange Symmetry in Multiqubit States under Ising Chain Evolution

Keeping in view of importance of exchange symmetry aspects in studies on spin squeezing of multiqubit states, we show that the one-dimensional Ising Hamiltonian with nearest neighbor interactions does not retain the exchange symmetry of initially symmetric multiqubit states. Specifically we show that among 4−qubit states obeying exchange symmetry, all states except W class (and their linear combination) lose their symmetry under time evolution with Ising Hamiltonian. Attributing the loss of symmetry of the initially symmetric states to rotational asymmetry of the one-dimensional Ising Hamiltonian with more than 3 qubits, we indicate that all N−qubit states (N≥5) obeying permutation symmetry lose their symmetry after time evolution with Ising Hamiltonian.