Classifying non-local quantum magic in partitions of many qubits

Non-local magic quantifies the non-stabilizerness of a quantum state encoded in correlations that span partitions of the Hilbert space, and serves as a key resource for achieving genuine quantum computational advantage. At the level of quantum operators, recent studies have revealed a correspondence between the entangling power of operators and their ability to generate non-local magic in a system. In this talk, we further investigate this operator perspective, exploring the distribution of non-local magic in the Hilbert space using a group-theoretic framework. We introduce the concept of a magic vector, which provides a complete description of the magic shared across all possible bipartitions of the Hilbert space, and establish fundamental bounds on the evolution of magic vectors under certain operator groups. Our results offer a mathematical framework for studying magic evolution under unitary evolution, offering new insights into the resource structure and efficient preparation of desired non-local magic states.