Magic, a quantum resource distinct from entanglement, measures departure from states stabilized by products of Pauli operators. Such stabilizer states can be maximally entangled yet admit efficient classical description: quantum advantage requires magic. We develop a powerful framework to evaluate the degree of magic in generic many-body states. We use it to study the fate of magic under thermal and dynamical evolution. In the transverse field Ising model, we find a thermal sudden death of magic that saturates with system size, and occurs after the death of entanglement. We reach similar conclusions in generic spin chains, and in the Kitaev quantum spin liquid on the honeycomb lattice, where the threshold shows an intricate dependence on subregion shape. We then study how magic equilibrates after a quantum quench. In quenches of generic spin chains, the magic of a subregion typically dies before entanglement, contrary to thermal trajectories. An explanation is given in terms of the geometry of non-magical states. As a third type of trajectory, we examine the fate of magic with separation with an appropriate notion of non-local magic and establish a sudden death. Finally, we show how to experimentally witness a volume law of frame-robust magic in quantum materials by using neutron scattering.
Local Markovian noise cannot bring entanglement back, but it can bring magic back. Unlike separability, stabilizer membership is not preserved by local channels, allowing dissipation to push states out of the stabilizer polytope as well as in. Under local amplitude damping, the
n-qubit GHZ family
α∣0n⟩+β∣1n⟩ (
0<α<β) loses its magic at a lower damping strength
γ− and regains it at a higher one
γ+, while entanglement is irreversibly lost at
γe. This magic--entanglement complementarity,
γe+γ+=1 for every
n, reflects a system--environment duality of amplitude damping. Within real phase-covariant Markovian semigroups the phenomenon is mapped out in full: zero-temperature rebirth occurs if and only if
T2>T1, unital dynamics produce no rebirth, and sufficiently weak thermal excitation confines rebirth to a finite magic island ending in a second sudden death. For small
α, the reborn magic resides in a fully separable state with all proper marginals stabilizer, yet parity-syndrome extraction concentrates it onto a single qubit for magic-state distillation, without loss of expected robustness and with optimal per-register yield
α2/2. Local dissipation further divides pure stabilizer states into magic-generators and magic-insulators: at two qubits, the Bell state
∣Φ+⟩ generates magic immediately, while its Bell-state partner
∣Ψ+⟩ remains stabilizer. Together, magic and entanglement reveal a symmetry invisible to either alone.
Quantum spin liquids (QSLs) are long-range entangled phases of matter and a natural setting for exploring how quantum correlations generate quantum complexity. Motivated by the emergence of magic, or nonstabilizerness, as a diagnostic of many-body complexity beyond entanglement, we study magic of QSLs by computing the stabilizer Rényi entropy (SRE) of the Kitaev honeycomb model. We derive a correspondence between Pauli strings and products of itinerant Majorana operators in the model's free-fermion description; this enables the sampling of SRE using an optimized algorithm for Gaussian states in systems with thousands of spins. Our results show that magic is largest in the gapless phase, where subleading volume-law corrections indicate nonlocal contributions, while in the gapped phases, SRE decreases in quantitative agreement with a perturbative expansion that we develop in the anisotropic limit. At the topological phase transition, SRE exhibits universal scaling dictated by critical exponents.
Stabilizer entropies and quantum magic have been extensively explored in real-space formulations of quantum systems within the framework of resource theory. However, interesting and transparent physics often emerges in momentum space, such as Cooper pairing. Motivated by this, we investigate the momentum-space structure of Pauli strings and stabilizer entropies in the one-dimensional transverse-field quantum Ising model. By mapping the Ising chain onto momentum-space qubits, where the stabilizer state corresponds to the paramagnetic state, we analyze the evolution of the Pauli string distribution. In the ferromagnetic phase, the distribution is broad, whereas in the paramagnetic phase, it develops a two-peaked structure. We demonstrate that all ferromagnetic states possess the same degree of magic in the thermodynamic limit, while stabilizer entropies are non-analytic at the critical point and vanish with increasing transverse field. The momentum-space approach to quantum magic not only complements its real-space counterpart but also provides advantages in terms of analyzing nonstabilizerness and classical simulability.
Physical many-body quantum systems typically interact locally, giving rise to ground states where entanglement grows with the area of the region being probed. Beyond entanglement, non-stabilizerness (or "magic") has been established as another crucial resource linked to quantum complexity and the properties of error-correcting states. Unlike entanglement, non-stabilizerness typically behaves with a volume-law scaling in ground states, indicating inherent computational complexity. In this work, we show that under a recent classification of quantum states, area-law states split into two distinct classes. Entanglement-dominated states obey an area-law for non-stabilizerness and admit efficient quantum algorithms for entanglement manipulation. Conversely, magic-dominated states exhibit a a faster-than-area growth of subsystem non-stabilizerness and require non-efficient algorithms for entanglement manipulation tasks. Within this context, we introduce the concept of the stabilizer regime, a restricted quantum phase that admits efficient entanglement manipulation and hosts area laws for both magic and entanglement.
Quantum many-body systems exhibit rich and complex behaviour. Magic has recently emerged as a powerful new diagnostic for probing such systems, complementing other key features such as many-body entanglement. Here, starting from an investigation of the onset of magic within subsystems of a larger many-body quantum system, we show that intricate structures emerge which shed important light on the underlying many-body physics. Focusing on the Kitaev honeycomb model, we first identify the temperature below which local subsystems acquire magic. Remarkably, we find that the optimal magic witnesses active at the onset of magic reveal compact operator spaces that continue to capture the local thermal states throughout their subsequent evolution. For the six-site hexagonal marginal, this connection can be made stronger: the same operator space emerges independently from the symmetries of the local marginal and forms the symmetry-resolved plaquette algebra. When these symmetries are realized exactly, the local state lies entirely within this algebra and the reduced robustness of magic is equal to the full robustness of magic. The same reduced description can also be applied to other local quantum resources, which we illustrate using genuine multipartite entanglement. Furthermore, the operator spaces possess a rich algebraic structure in the form of finite-dimensional Euclidean Jordan algebras, with a natural interpretation in terms of bond and bond-cycle operators. Our general methodology therefore show how the onset of local magic can reveal a compact, physically meaningful operator structure underlying the finite-temperature Kitaev spin liquid, and opens up a new avenue towards reduced descriptions of quantum resources in many-body systems.
We study the behavior of magic as a bipartite correlation in the quantum Ising chain across its quantum phase transition and at finite temperature. To quantify the magic of partitions rigorously, we formulate a hybrid scheme that combines stochastic sampling of reduced density matrices via quantum Monte Carlo, with state-of-the-art estimators for the robustness of magic - a bona fide measure of magic for mixed states. This allows us to compute the mutual robustness of magic for partitions up to eight sites, embedded into a much larger system. We show how mutual robustness is directly related to critical behaviors: at the critical point, it displays a power-law decay as a function of the distance between partitions, whose exponent is related to the partition size. Once finite temperature is included, mutual magic retains its low temperature value up to an effective critical temperature, whose dependence on size is also algebraic. This suggests that magic, differently from entanglement, does not necessarily undergo a sudden death.