Related papers: Quantization as a Categorical Equivalence
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…
In recent work, symmetric dagger-monoidal (SDM) categories have emerged as a convenient categorical formalization of quantum mechanics. The objects represent physical systems, the morphisms physical operations, whereas the tensors describe…
Quantum categories were introduced in [4] as generalizations of both bi(co)algebroids and small categories. We clarify details of that work. In particular, we show explicitly how the monadic definition of a quantum category unpacks to a set…
Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…
This paper revisits the equivalence problem between algebraic quantum field theories and prefactorization algebras defined over globally hyperbolic Lorentzian manifolds. We develop a radically new approach whose main innovative features are…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Relational quantum queries are sometimes capable to effectively decide between collections of mutually exclusive elementary cases without completely resolving and determining those individual instances. Thereby the set of mutually exclusive…
The so-called classical limit of quantum mechanics is generally studied in terms of the decoherence of the state operator that characterizes a system. This is not the only possible approach to decoherence. In previous works we have…
This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation,…
Many types of categorical structure obey the following principle: the natural notion of equivalence is generated, as an equivalence relation, by identifying $A$ with $B$ when there exists a strictly structure-preserving map $A \to B$ that…
We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A-infinity functor categories arise as internal Hom-objects in the category of differential graded…
Some connections between quantum mechanics and classical physics are explored. The Planck-Einstein and De Broglie relations, the wavefunction and its probabilistic interpretation, the Canonical Commutation Relations and the Maxwell--Lorentz…
We show that the class of quantum baker's maps defined by Schack and Caves have the proper classical limit provided the number of momentum bits approaches infinity. This is done by deriving a semi-classical approximation to the…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
Two quantum theories are physically equivalent if they are related, not by a unitary transformation, but by an isometric transformation. The conditions under which a quantum canonical transformation is an isometric transformation are given.