Related papers: Invariants, Kronecker Products, and Combinatorics …
This paper is a survey of knot theory and invariants of knots and links from the point of view of categories of diagrams. The topics range from foundations of knot theory to virtual knot theory and topological quantum field theory.
Various topics concerning the entanglement of composite quantum systems are considered with particular emphasis concerning the strict relations of such a problem with the one of attributing objective properties to the constituents. Most of…
Quantum theory departs from classical probabilistic theories in foundational ways. These departures--termed quantumness here--power quantum information and computation. This thesis charts the role of discrete structures in assessing…
Quantum coherence is a fundamental characteristic to distinguish quantum systems from their classical counterparts. Though quantum coherence persists in isolated non-interacting systems, interactions inevitably lead to decoherence, which is…
We study Coxeter racks over $\mathbb{Z}_n$ and the knot and link invariants they define. We exploit the module structure of these racks to enhance the rack counting invariants and give examples showing that these enhanced invariants are…
This article presents new colored link invariants by introducing the concepts of multi-quandles and topological multi-quandles.
Quantization of diffeomorphism invariant theories of connections is studied. A solutions of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality…
Mixed state quantum computation can perform certain tasks which are believed to be efficiently intractable on a classical computer. For a specific model of mixed state quantum computation, namely, {\it deterministic quantum computation with…
Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present these…
If a one-phrase summary of the subject of this thesis were required, it would be something like: miscellaneous large (but finite) dimensional phenomena in quantum information theory. That said, it could nonetheless be helpful to briefly…
We study different notions of quantum correlations in multipartite systems of distinguishable and indistinguishable particles. Based on the definition of quantum coherence for a single particle, we consider two possible extensions of this…
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit…
We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…
A q-deformed version of classical analysis is given to quantum spaces of physical importance, i.e. Manin plane, q-deformed Euclidean space in three or four dimensions, and q-deformed Minkowski space. The subject is presented in a rather…
We introduce new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union of two identical surfaces. The invariants are constructed via surgery on manifolds of the form $F \times I$…
Students of quantum mechanics encounter discrete quantum numbers in a somewhat incoherent and bewildering number of ways. For each physical system studied, quantum numbers seem to be introduced in its own specific way, some enumerating from…
Quantum coherence is a fundamental property of quantum systems, separating quantum from classical physics. Recently, there has been significant interest in the characterization of quantum coherence as a resource, investigating how coherence…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…