(Long-range) Magic on the Information Lattice

The information lattice provides a decomposition of information in a quantum state into position and scale, thereby providing a definition of local information. This decomposition provides a universal categorization of many-body quantum states based on the structure of the local information. I will demonstrate this for the various phases of an interacting Kitaev model. The special class of stabilizer states feature integer local information related to the measurement of a minimal set of maximally localized stabilizers. The deviation of a state from a stabilizer state is referred to as nonstabilizerness or magic. For states with a separation in scales for the local information, we show how to use the information lattice to diagnoze long-range nonstabilizerness.