Related papers: Projective characterization of higher-order quantu…
A general framework is presented which unifies the treatment of wavelet-like, quasidistribution, and tomographic transforms. Explicit formulas relating the three types of transforms are obtained. The case of transforms associated to the…
Machine learning models are a powerful theoretical tool for analyzing data from quantum simulators, in which results of experiments are sets of snapshots of many-body states. Recently, they have been successfully applied to distinguish…
In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective…
We promote geometric prequantization to higher geometry (higher stacks), where a prequantization is given by a higher principal connection (a higher gerbe with connection). We show fairly generally how there is canonically a tower of higher…
The modern framework of state transformers, i. e., the first Kraus representation of quantum measurement, is introduced and related both to the known textbook concepts and to measurement-interaction evolution (the second Kraus…
Considering homogeneous four-dimensional space-time geometries within real projective geometry provides a mathematically well-defined framework to discuss their deformations and limits without the appearance of coordinate singularities. On…
Algebraic effect handlers is a programming paradigm where programmers can declare their own syntactic operations, and modularly define the semantics of these using effect handlers. However, we cannot directly define algebraic effect…
We introduce a construction that turns a category of pure state spaces and operators into a category of observable algebras and superoperators. For example, it turns the category of finite-dimensional Hilbert spaces into the category of…
Projective metrics on vector spaces over finite fields, introduced by Gabidulin and Simonis in 1997, generalize classical metrics in coding theory like the Hamming metric, rank metric, and combinatorial metrics. While these specific metrics…
Reductions of higher tangent bundles of Lie groupoids provide natural examples of geometric structures which we would like to call higher algebroids. Such objects can be also constructed abstractly starting from an arbitrary almost Lie…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
The Desargues property is well known in the context of projective geometry. An analogous property is presented in the context of both classical and Quantum Physics. In a classical context, the Desargues property implies that two logical…
Some introductory concepts and basic definitions of the Lie superalgebras and their quantum deformations are exposed. Especially the induced representation methods in both cases are described. Based on the Kac representation theory we have…
In quantum computing, knowing the symmetries a given system or state obeys or disobeys is often useful. For example, Hamiltonian symmetries may limit allowed state transitions or simplify learning parameters in machine learning…
Normalization and scaling are fundamental preprocessing steps in time series modeling, yet their role in Transformer-based models remains underexplored from a theoretical perspective. In this work, we present the first formal analysis of…
The quantum mechanical formalism doesn't support our intuition, nor does it elucidate the key concepts that govern the behaviour of the entities that are subject to the laws of quantum physics. The arrays of complex numbers are kin to the…
We show that, when the actions of a Mazurkiewicz trace are considered not merely as atomic (i.e., mere names) but transformations from a specified type of inputs to a specified type of outputs, we obtain a novel notion of presentation for…
We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically…
We generalize the standard first-order intertwining relationship of supersymmetric quantum mechanics in order to include simultaneous scaling transformations in both the original Hamiltonian and the intertwining operator. It is argued that…
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…