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The understanding and manipulation of information at quantum level requires an adequate treatment of phenomena such as qubits stability, singular behavior of Fidelity evolution at the event of quantum phase transitions, tunneling, and parametric dependence of physical observables, such as the magnetization, under control variables manipulation. In the present work we consider the Lipkin–Meshkov–Glick model Hamiltonian, useful in the treatment of a kind of single-molecule magnets. Phase transition behavior is treated by means of catastrophe theory. We show that quantum and semiclassical behavior are completely organized by the separatrix of the system. Catastrophe theory and the coherent states formalism represent powerful tools in the analytical treatment of quantum information and its semiclassical behavior. Coherent states of the model demonstrate their importance at the semiclassic critical points. In particular, these states represent very closely the ground state of the system. Coherent qubit states are introduced by means of the coherent state representation of the system states. Singular character of Fidelity, due to tunneling at a phase transition point, can be numerically adjusted very closely to a Lorentzian curve.

Coherent qubits stability and quantum phase transitions in the Lipkin–Meshkov–Glick model