Related papers: Algebraic Approach to Interacting Quantum Systems
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
A proposal of an algebraic model for the relation between a quantum environment and certain classical particle system is given. The quantum environment is described by a category of possible quantum states, the initial particle system is…
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
We introduce a Geometry of Interaction model for higher-order quantum computation, and prove its adequacy for a full quantum programming language in which entanglement, duplication, and recursion are all available. Our model comes with a…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those with…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
This document is meant as a pedagogical introduction to the modern language used to talk about quantum theory, especially in the field of quantum information. It assumes that the reader has taken a first traditional course on quantum…
Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…
Within the C*-algebraic framework of the resolvent algebra for canonical quantum systems, the structure of oscillating lattice systems with bounded nearest neighbor interactions is studied in any number of dimensions. The global dynamics of…
Recently, an {\it algebraic-dynamical theory} (ADT) for strongly interacting many-body quantum Hamiltonians in W. Ding, arXiv: 2202.12082 (2022). By introducing the complete operator basis set, ADT proposes a generic framework for…
The algebraic approach to quantum physics emphasizes the role played by the structure of the algebra of observables and its relation to the space of states. An important feature of this point of view is that subsystems can be described by…
We study improper mixtures from a quantum logical and geometrical point of view. Taking into account the fact that improper mixtures do not admit an ignorance interpretation and must be considered as states in their own right, we do not…
While much of the current study on quantum computation employs low-level formalisms such as quantum circuits, several high-level languages/calculi have been recently proposed aiming at structured quantum programming. The current work…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
An algebraic approach to the study of quantum mechanics on configuration spaces with a finite fundamental group is presented. It uses, in an essential way, the Gelfand-Naimark and Serre-Swan equivalences and thus allows one to represent…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…