Related papers: Quantum structures from association schemes

The possibility of simulating a stochastic process by the intrinsic randomness of quantum system is investigated. Two simulations of Markov Chains by the measurements of quantum systems are proposed.

An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…

In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own…

We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these…

The measurement-based architecture is a paradigm of quantum computing, relying on the entanglement of a cluster of qubits and the measurements of a subset of it, conditioning the state of the unmeasured output qubits. While methods to map…

We construct representations of a q-oscillator algebra by operators on Fock space on positive matrices. They emerge from a multiresolution scaling construction used in wavelet analysis. The representations of the Cuntz Algebra arising from…

We define a new mathematical structure ( graph quantum group) which combines the tower of algebras associated with a graph ${\cal G}$ and the structure of a Hopf algebra {\cal A}. In this structure Ocneanu's string operators become Hopf…

Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and…

A recently introduced numerical approach to quantum systems is analyzed. The basis of a Fock space is restricted and represented in an algebraic program. Convergence with increasing size of basis is proved and the difference between…

We present a novel approach to quantizing Markov chains. The approach is based on the Markov chain coupling method, which is frequently used to prove fast mixing. Given a particular coupling, e.g., a grand coupling, we construct a…

We point to the connection between a recently introduced class of non-Markovian master equations and the general structure of quantum collisional models. The basic construction relies on three basic ingredients: a collection of time…

The symmetrization postulate and the associated Bose/Fermi (anti)-commutators for field mode operators are among the pillars on which local quantum field theory lays its foundations. They ultimately determine the structure of Fock space and…

Random intersection graphs have received much interest and been used in diverse applications. They are naturally induced in modeling secure sensor networks under random key predistribution schemes, as well as in modeling the topologies of…

These lecture notes cover 13 sessions and are presented as an e-print, intended to evolve over time. Quantum invariants do more than distinguish topological objects; they build bridges between topology, algebra, number theory and quantum…

In this paper we show how to generalize the quantum approximate counting technique developed by Brassard, H{\o}yer and Tapp [ICALP 1998] to a more general setting: estimating the number of marked states of a Markov chain (a Markov chain can…

Beginning with a skew-symmetric matrix, we define a certain Poisson--Lie group. Its Poisson bracket can be viewed as a cocycle perturbation of the linear (or "Lie-Poisson") Poisson bracket. By analyzing this Poisson structure, we gather…

We study one-dimensional quantum gases in continuous space with cavity-mediated infinite-range interactions using variational and diffusion Monte Carlo methods. Starting from the exact two-body solution, we construct a non-translationally…

This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…

We provide a class of positive and trace-preserving maps based on symmetric measurements. From these positive maps we present separability criteria, entanglement witnesses, as well as the lower bounds of concurrence. We show by detailed…