A quantum computer relies on two forces: entanglement (particles behaving as a single whole) and "magic"—a measure of how far a state is from familiar classical physics. But how these two resources relate as a many-particle system evolves in time has remained a puzzle.

The authors approached the problem through time. They compared the moment of fastest entanglement growth with the moment when the "magic barrier" peaks — a characteristic of the entanglement spectrum that shows its deviation from flatness. If entanglement is born locally, through neighboring particles interacting, both peaks arrive almost simultaneously. If it is mostly transferred or redistributed across the system, the entropy growth peak comes earlier, and the magic barrier later.

The idea was tested on a chain of spins in a random magnetic field (the XXZ model). In the thermal regime, where particles actively exchange energy, the peaks remained close. But when transitioning to many-body localization (MBL), where energy transfer freezes, the gap between peaks grew systematically. The theory was further confirmed on a tunable circuit of Bell pairs and random permutations.

Thus, the "magic barrier" becomes a diagnostic tool. The divergence of peaks hints whether quantum complexity is born on the spot or arrives from other parts of the system.