Probing quantum complexity via universal saturation of stabilizer entropies

Understand

Nonstabilizerness or `magic' is a key resource for quantum computing and a necessary condition for quantum advantage.

• Non-Clifford operations turn stabilizer states into resourceful states, where the amount of nonstabilizerness is quantified by resource measures such as stabilizer R\'enyi entropies (SREs).
• Here, we show that SREs saturate their maximum value at a critical number of non-Clifford operations.
• Close to the critical point SREs show universal behavior.