Related papers: Anyons and matrix product operator algebras
We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization…
We review the q-deformed spin network approact to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. These methods produce a concise proof…
It is well known that the abelian $Z_2$ anyonic model (toric code) can be realized on a highly entangled two-dimensional spin lattice, where the anyons are quasiparticles located at the endpoints of string-like concatenations of Pauli…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
We analyze the Namioka-Phelps minimal and maximal tensor products of compact convex sets arising as state spaces of C$^*$-algebras, and, relatedly, study entanglement in (infinite dimensional) C$^*$-algebras. The minimal Namioka-Phelps…
In this semi-expository paper, we first explain key notions from current quantum information theory and criteria for them in a coherent way. These include separability/entanglement, Schmidt numbers of bi-partite states and block-positivity,…
Braiding operators corresponding to the third Reidemeister move in the theory of knots and links are realized in terms of parametrized unitary matrices for all dimensions. Two distinct classes are considered. Their (non-local) unitary…
This is the third part in a series of papers developing a tensor product theory for modules for a vertex operator algebra. The goal of this theory is to construct a ``vertex tensor category'' structure on the category of modules for a…
We review recent interactions between mathematical theory of two-dimensional topological order and operator algebras, particularly the Jones theory of subfactors. The role of representation theory in terms of tensor categories is…
This thesis is divided into two mainly independent parts: In the first part, we derive a criterion to determine when a translationally invariant Matrix Product State (MPS) has long range localizable entanglement, which indicates that the…
We use Projected Entangled Pair States (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement…
We describe how self-adjoint ordered operator spaces, also called non-unital operator systems in the literature, can be understood as $*$-vector spaces equipped with a matrix gauge structure. We explain how this perspective has several…
Quantum computation is based on tensor products and entangled states. We discuss an alternative to the quantum framework where tensor products are replaced by geometric products and entangled states by multivectors. The resulting theory is…
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and q-alg/9505020 to the case of the…
Quantum computing is arguably one of the most revolutionary and disruptive technologies of this century. Due to the ever-increasing number of potential applications as well as the continuing rise in complexity, the development, simulation,…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
The benefits of exploiting the presence of symmetries in tensor network algorithms have been extensively demonstrated in the context of matrix product states (MPSs). These include the ability to select a specific symmetry sector (e.g. with…
We construct explicit approximating nets for crossed products of C*-algebras by actions of discrete quantum groups. This implies that C*-algebraic approximation properties such as nuclearity, exactness or completely bounded approximation…
In spite of their intrinsic one-dimensional nature matrix product states have been systematically used to obtain remarkably accurate results for two-dimensional systems. Motivated by basic entropic arguments favoring projected…
One of the apparent advantages of quantum computers over their classical counterparts is their ability to efficiently contract tensor networks. In this article, we study some implications of this fact in the case of topological tensor…