Generalized W States and Nonlocal Magic
Abstract
The complexity of quantum simulations does not arise from entanglement alone. The key aspect of the complexity of the quantum state is shown to be related to non-stabilizerness or magic. The Gottesman-Knill theorem shows that even some highly entangled states can be simulated efficiently. Therefore, magic is a resource and represents the amount of non-Clifford operations (e.g. T-gates) needed to prepare a quantum state. We demonstrate, using Stabilizer Renyi Entropy, that degenerate quantum many-body grounds states with nonzero lattice momentum admit an increment of magic compared to a state with zero momentum. We quantify this increment analytically and show how finite momentum does not only increase the long-range entanglement but also leads to a change in magic. Additionally, we provide a connection between the W state and its generalizations, frequently discussed in the quantum information community, and ground states of frustrated spin chains.
