Boundary time crystals exhibit measurement-induced phase transitions in their steady-state entanglement, with critical behavior that depends on the particular unraveling of the Lindblad dynamics. In this work, we investigate another key measure of quantum complexity—nonstabilizerness (or “magic”)—and show that it follows a markedly different pattern. Importantly, in contrast to entanglement, for large system sizes, nonstabilizerness remains invariant under different unraveling schemes—a property we attribute to the inherent permutational symmetry of the model. Although the steady-state stabilizer entropy does not display a genuine phase transition, it exhibits a singular derivative (a cusp) at the mean-field critical point. Furthermore, we demonstrate that finite-size simulations of the average Lindblad evolution fail to capture the asymptotic behavior of nonstabilizerness in the time-crystal phase, while quantum trajectory unravelings correctly reveal its extensive scaling with system size. These findings offer insights into how different quantum resources manifest in open systems.

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• Dissipative dynamics
• Quantum correlations in quantum information
• Resource theories
• Time crystals