Related papers: Quantum Tomography and the Quantum Radon Transform
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear…
The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic…
Topological holography is a holographic principle that describes the generalized global symmetry of a local quantum system in terms of a topological order in one higher dimension. This framework separates the topological data from the local…
We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative…
It is shown how a C*-algebra representation of the transformations of a physical system can be derived from two operational postulates: 1) the existence of dynamically independent systems}; 2) the existence of symmetric faithful states.…
We explore the main processes involved in the evolution of general quantum systems by means of Diagrams of States, a novel method to graphically represent and analyze how quantum information is elaborated during computations performed by…
Characterizing quantum systems is a fundamental task that enables the development of quantum technologies. Various approaches, ranging from full tomography to instances of classical shadows, have been proposed to this end. However, quantum…
We sketch our recent application of a non-commutative version of the Cartan `moving-frame' formalism to the quantum Euclidean space $R^N_q$, the space which is covariant under the action of the quantum group $SO_q(N)$. For each of the two…
Using projections on the (generalized) eigenvectors associated to matrices that characterize the topological structure, several authors have constructed generalizations of the Fourier transform on graphs. By exploring mappings of the…
We show that certain C*-algebras which have been studied among others by Arzumanian, Vershik, Deaconu, and Renault in connection to a measure preserving transformation of a measure space and/or to a covering map of a compact space are…
Quantum state tomography is a fundamental task in quantum information science, enabling detailed characterization of correlations, entanglement, and electronic structure in quantum systems. However, its exponential measurement and…
We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is…
Within the framework of the probability representation of quantum mechanics, we study a superposition of generic Gaussian states associated to symmetries of a regular polygon of n sides; in other words, the cyclic groups (containing the…
To obtain a complete description of a quantum system, one usually employs standard quantum state tomography, which however requires exponential number of measurements to perform and hence is impractical when the system's size grows large.…
Quantum state tomography (QST) is a fundamental task in quantum information science that aims to reconstruct unknown quantum states from measurement data. However, the exponential growth of Hilbert-space dimension with system size makes…
We study different techniques that allow us to gain complete knowledge about an unknown quantum state, e.g. to perform full tomography of this state. We focus on two apparently simple cases, full tomography of one and two qubit systems. We…
Linearity allows several versions of reality to simultaneously exist in the state vector. But it implies that there is no interaction between versions, and that there will never be perception of more than one version. It also implies, in…
We extend the algebraic diversity (AD) framework from classical signal processing to quantum measurement theory. The central result -- the Quantum Algebraic Diversity (QAD) Theorem -- establishes that a group-structured positive…