Many-body magic via Pauli-Markov chains -- from criticality to gauge theories

Understand

We introduce a method to measure many-body magic in quantum systems based on a statistical exploration of Pauli strings via Markov chains.

• We demonstrate that sampling such Pauli-Markov chains gives ample flexibility in terms of partitions where to sample from: in particular, it enables to efficiently extract the magic contained in the correlations between widely-separated subsystems, which characterizes the nonlocality of magic.
• Our method can be implemented in a variety of situations.
• We describe an efficient sampling procedure using Tree Tensor Networks, that exploits their hierarchical structure leading to a modest $O(\log N)$ computational scaling with system size.