This is a PhD Thesis on the connection between subfactors (more precisely, their
corresponding fusion categories) and Conformal Field Theory (CFT). Besides being a …

We present a generalization of the quantum volume operator quantifying the volume in
curved three-dimensional discrete geometries. In its standard form, the quantum volume …

The topological entanglement entropy is used to measure long-range quantum correlations
in the ground space of topological phases. Here we obtain closed form expressions for the …

Matrix product density operators (MPDOs) are an important class of states with interesting
properties. Consequently, it is important to understand how to prepare these states …

The aim of the paper is to assess the relative merits of two formal representations of
structure, namely, set theory and category theory. The purpose is to articulate ontic structural …

Topological order is a special kind of quantum order which appears in strongly interacting
gappedquantum systems and does not admit a description by a local order parameter and …

Almost all phenomena in the universe are described, at the fundamental level, by quantum
manybody models. In general, however, a complete understanding of large systems with …

Entangled possibly mixed states are an essential resource for quantum computation,
communication, metrology, and the simulation of many-body systems. It is important to …

The computation of correlation functions in models of statistical mechanics is the key to
comparing theoretical results with actual measurements. In the context of integrable lattice …

[en] Topological quantum computation is an approach to quantum computation that employs
exotic quasiparticles, called anyons, to store and manipulate quantum information. Anyons …