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Motivated by the novel applications of the mathematical formalism of quantum theory and its generalizations in cognitive science, psychology, social and political sciences, and economics, we extend the notion of the tensor product and…
We introduce a general theory of parametrized objects in the setting of infinity categories. Although spaces and spectra parametrized over spaces are the most familiar examples, we establish our theory in the generality of objects of a…
From the generating matrix of a linear code one can construct a sequence of generalized star configurations which are strongly connected to the generalized Hamming weights and the underlying matroid of the code. When the code is MDS, the…
The technologies of quantum information and quantum control are rapidly improving, but full exploitation of their capabilities requires complete characterization and assessment of processes that occur within quantum devices. We present a…
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita connection. The construction of a natural…
A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
The thesis showcases the importance of tomograms in quantifying nonclassical effects such as wavepacket revivals, squeezing, and quantum entanglement in continuous-variable, hybrid quantum, and qubit systems. This approach avoids…
Quantum computers are designed to outperform standard computers by running quantum algorithms. Areas in which quantum algorithms can be applied include cryptography, search and optimisation, simulation of quantum systems, and solving large…
We define several new types of quantum chromatic numbers of a graph and characterise them in terms of operator system tensor products. We establish inequalities between these chromatic numbers and other parameters of graphs studied in the…
Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical…
A notion of a quantum automorphism group of a finite quantum group, generalising that of a classical automorphism group of a finite group, is proposed and a corresponding existence result proved.
Theories of natural language and concepts have been unable to model the flexibility, creativity, context-dependence, and emergence, exhibited by words, concepts and their combinations. The mathematical formalism of quantum theory has…
Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end,…
We study quantum moment maps of $G$-invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a $G$-invariant…
Amongst the multitude of state reconstruction techniques, the so-called "quantum tomography" seems to be the most fruitful. In this letter, I will start by developing the mathematical apparatus of quantum tomography and, later, I will…
In this article we propose a new approach to quantum measurement in reference to the stroboscopic tomography. Generally, in the stroboscopic approach it is assumed that the information about the quantum system is encoded in the mean values…
Starting from a new principle inspired by quantum tomography rather than from Born's rule, this paper gives a self-contained deductive approach to quantum mechanics and quantum measurement. A suggestive notion for what constitutes a quantum…
We overcome one of Bell's objections to `quantum measurement' by generalizing the definition to include systems outside the laboratory. According to this definition a {\sl generalized quantum measurement} takes place when the value of a…
Convolution is an important tool in the construction of positive definite kernels on a manifold. This contribution provides conditions on an $L^2$-positive definite and zonal kernel on the unit sphere of $\mathbb{C}^q$ in order that the…