Momentum space magic for the transverse field quantum Ising model

Abstract

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.