Related papers: Quantum Tomography and the Quantum Radon Transform
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
We define and study an analogue of the Baum-Connes assembly map for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. Our starting point is the deformation picture of the…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
Various reconstructions of finite-dimensional quantum mechanics result in a formally real Jordan algebra A and a last step remains to conclude that A is the self-adjoint part of a C*-algebra. Using a quantum logical setting, it is shown…
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in…
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 give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix. Under low-rank assumptions, the remaining entries can be…
The tomographic representation of quantum fields within the deformation quantization formalism is constructed. By employing the Wigner functional we obtain the symplectic tomogram associated with quantum fields. In addition, the tomographic…
Given an ample groupoid $G$ with compact unit space, we study the canonical representation of the topological full group $[[G]]$ in the full groupoid $C^*$-algebra $C^*(G)$. In particular, we show that the image of this representation…
With the ability to directly obtain the Wigner function and density matrix of photon states, quantum tomography (QT) has had a significant impact on quantum optics, quantum computing and quantum information. By an appropriate sequence of…
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…
Ultrafast electron diffraction and time-resolved serial crystallography are the basis of the ongoing revolution in capturing at the atomic level of detail the structural dynamics of molecules. However, most experiments employ the classical…
Tomograms, a generalization of the Radon transform to arbitrary pairs of non-commuting operators, are positive bilinear transforms with a rigorous probabilistic interpretation which provide a full characterization of the signal and are…
Quantum operations describe any state change allowed in quantum mechanics, including the evolution of an open system or the state change due to a measurement. In this letter we present a general method based on quantum tomography for…
In [J. Bures, R. Lavicka, V. Soucek, Elements of quaternionic analysis and Radon transform, Textos de Matematica 42, Departamento de Matematica, Universidade de Coimbra, 2009], the authors describe a link between holomorphic functions…
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
These lecture notes give an introduction to the mathematics of computer(ized) tomography (CT). Treated are the imaging principle of X-ray tomography, the Radon transform as mathematical model for the measurement process and its properties,…
We analyze the tomographic representation for the Friedmann-Robertson-Walker (FRW) model within the Loop Quantum Cosmology framework. We focus on the Wigner quasi-probability distributions associated with Gaussian and Schr\"odinger cat…