相关论文: Quantum Classifying Spaces and Universal Quantum C…
We provide a new characterisation of quantum supermaps in terms of an axiom that refers only to sequential and parallel composition. Consequently, we generalize quantum supermaps to arbitrary monoidal categories and operational…
An idealized experiment estimating the spacetime topology is considered in both classical and quantum frameworks. The latter is described in terms of histories approach to quantum theory. A procedure creating combinatorial models of…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
A discursive, non-technical, analysis is made of some of the basic issues that arise in almost any approach to quantum gravity, and of how these issues stand in relation to recent developments in the field. Specific topics include the…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we…
Quantum algorithms are sequences of abstract operations, performed on non-existent computers. They are in obvious need of categorical semantics. We present some steps in this direction, following earlier contributions of Abramsky, Coecke…
In quantum geometry, we consider a set of loops, a compact orientable surface and a solid compact spatial region, all inside $\mathbb{R} \times \mathbb{R}^3 \equiv \mathbb{R}^4$, which forms a triple. We want to define an ambient isotopic…
Classical and quantum world views differ in peculiar ways. Understanding decisive quantum features -- for which no classical explanation exist -- and their interrelations is of foundational interest. Moreover, recognizing non-classical…
The aim of this paper is to analyze the reconstructability of quantum mechanics from classical conditional probabilities representing measurement outcomes conditioned on measurement choices. We will investigate how the quantum mechanical…
The aim of this paper is to survey some aspects of mapping class groups with focus on their finite dimensional representations arising in topological quantum field theory.
A one-to-one correspondence is established between linearized space-time metrics of general relativity and the wave equations of quantum mechanics. Also, the key role of boundary conditions in distinguishing quantum mechanics from classical…
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
These notes are an introduction to the theory of quantum symmetries of finite and infinite sets, graphs, and locally compact spaces.
The groupoid approach to noncommutative unification of general relativity with quantum mechanics is compared with the canonical gravity quantization. It is shown that by restricting the corresponding noncommutative algebra to its…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
Quantum Computing and especially Quantum Machine Learning, in a short period of time, has gained a lot of interest through research groups around the world. This can be seen in the increasing number of proposed models for pattern…
We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…