William Munizzi

A bstract: We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in SU (2) ₁ Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions, enabling an explicit topological realization of W _n and Dicke states, as well as their entanglement properties. For the genus-1 case, the modular SL (2 , ℤ) generators on a single torus boundary realize the standard Clifford generators. We further conjecture a higher-genus extension of this correspondence specifically for the Clifford orbits of W and Dicke states, in which the orbit of W _n is represented by a sum over genus- g handlebodies with Dehn twists applied to each torus. Our results extend the known correspondence between Clifford structures and modular transformations, and demonstrate that non-stabilizer states can be understood as controlled deformations within the SU (2) ₁ modular tensor category, providing a concrete example of how non-stabilizer quantum resources emerge from purely topological data.

We study the interplay between magic and entanglement in quantum many-body systems. We show that nonlocal magic, which is supported by the quantum correlations is lower bounded by the nonflatness of entanglement spectrum and upper bounded by the amount of entanglement in the system. We then argue that a smoothed version of nonlocal magic bounds the hardness of classical simulations for incompressible states. In conformal field theories (CFTs), we conjecture that the nonlocal magic should scale linearly with entanglement entropy but sublinearly when an approximation of the state is allowed. We support the conjectures using both analytical arguments based on unitary distillation and numerical data from an Ising CFT. If the CFT has a holographic dual, then we prove that the nonlocal magic vanishes if and only if there is no gravitational backreaction. Furthermore, we show that nonlocal magic is approximately equal to the rate of change of the minimal surface area in response to the change of cosmic brane tension in the bulk.

The monogamy of mutual information (MMI) is a quantum entropy inequality that enforces the non-positivity of tripartite information. We investigate the failure of MMI in graph states as a forbidden-subgraph phenomenon, conjecturing that every MMI-violating graph state is local-Clifford equivalent to one whose graph contains a four-star subgraph. We construct a family of star-like graphs whose states fail a specific class of MMI instances, and extend this analysis to general star topologies. Deriving adjacency matrix constraints that fix the MMI evaluation for these instances and interpreting them physically, we prove the forbidden-subgraph conjecture for this family of graphs. Finally, through an exhaustive search over graph representatives for all $8$-qubit stabilizer entropy vectors, we establish that MMI failure is not reducible to the cases within our scope.

We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, focusing on violations of entropy inequalities. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that optimally navigate the entropy vector space to generate violations of Ingleton's inequality. We complement this approach with a classical optimization algorithm to produce arbitrary numbers of Ingleton-violating states, with tunable degrees of violation, and empirically determine the maximal attainable violation for Ingleton's inequality. Our analysis reveals characteristic patterns of quantum resources that accompany Ingleton violation. A comprehensive statistical analysis shows that Ingleton-violating states occupy sharply-defined, isolated regions of the Hilbert space, and are extremely rare. Together, these results establish a unified computational toolkit for studying entropy vector dynamics, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features.

In this work we apply the lightcone bootstrap to a four-point function of scalars in two-dimensional conformal field theory. We include the entire Virasoro symmetry and consider non-rational theories with a gap in the spectrum from the vacuum and no conserved currents. For those theories, we compute the large dimension limit (h/c>>1) of the OPE spectral decomposition of the Virasoro vacuum. We then propose a kernel ansatz that generalizes the spectral decomposition beyond h/c>>1. Finally, we estimate the corrections to the OPE spectral densities from the inclusion of the lightest operator in the spectrum.