  Projected squeezed (PS) states are multipartite entangled states generated by
unitary spin squeezing, followed by a collective quantum measurement and
post-selection. They can lead to an appreciable decrease in the state
preparation time of the maximally entangled N-qubit Greenberger-Horne-Zeilinger
(GHZ) state when compared to deterministic preparation by unitary
transformations in physical systems where spin squeezing can be realized, such
as ion, neutral atom, and superconducting qubits. Here we simulate the
generation of PS states in non-ideal experimental conditions with relevant
decoherence channels. By employing the Kraus operator method, and quantum
trajectory method to reduce the computational complexity, we assess the quantum
Fisher information and overlap fidelity with an ideal GHZ state. Our findings
highlight PS states as useful metrological resources, demonstrating a
robustness against environmental effects with increasing qubit number N.
