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.
as written by the authors arXiv:2607.09875
Quantum entanglement and magic are complementary resources underlying quantum computational advantage, yet their dynamical relation in many-body systems remains poorly understood. In this Letter, we show that the mechanism of bipartite entanglement growth is encoded in the relative timescale between the entropy-growth-rate peak and the magic barrier, defined as the transient peak of the anti-flatness of the entanglement spectrum. When entanglement is locally built, the same microscopic process increases the entropy and reshapes the Schmidt spectrum, so the magic-barrier peak occurs in the time window of maximal entropy growth. When entanglement is mainly transported or redistributed, entropy can grow before appreciable spectral non-flatness is generated, naturally separating the two peak times. We demonstrate this distinction in the random-field XXZ chain: the two peaks remain strongly correlated in the thermal regime, while their separation grows systematically across the thermal--MBL crossover. We further validate this theoretical framework by employing Bell-pair initial states alongside a tunable SWAP--Haar random circuit. Our results reveal an intrinsic dynamical connection between entanglement and magic, establishing the magic barrier as a powerful spectral diagnostic of how quantum information is generated, transported, and reshaped.
The word "magic" in quantum physics started as a joke: it was named the resource needed for quantum supremacy because without it, computations become "too easy."