Related papers: Generalized quantum tomographic maps
By reformulating Wang tiles with tensors, we propose a natural generalization to the probabilistic and quantum setting. In this new framework, we introduce notions of tilings and periodicity directly extending their classical counterparts.…
Quantum state tomography, the ability to deduce the state of a quantum system from measured data, is the gold standard for verification and benchmarking of quantum devices. It has been realized in systems with few components, but for larger…
Inspired by classical ("actual") Quantum Theory over $\mathbb{C}$ and Modal Quantum Theory (MQT), which is a model of Quantum Theory over certain finite fields, we introduce General Quantum Theory as a Quantum Theory -- in the K{\o}benhavn…
Reconstructing the state of a complex quantum system represents a pivotal task for all quantum information applications, both for characterization purposes and for verification of quantum protocols. Recent technological developments have…
Tomography is an indispensable part of quantum computation as it enables diagnosis of a quantum process through state reconstruction. Existing tomographic protocols are based on determining expectation values of various Pauli operators…
Tomograms are obtained as probability distributions and are used to reconstruct a quantum state from experimentally measured values. We study the evolution of tomograms for different quantum systems, both finite and infinite dimensional. In…
A general framework is described which associates geometrical structures to any set of $D$ finite-dimensional hermitian matrices $X^a, \ a=1,...,D$. This framework generalizes and systematizes the well-known examples of fuzzy spaces, and…
We present the general theory of relativity in the language of a non-Riemannian geometry, namely, Weyl geometry. We show that the new mathematical formalism may lead to different pictures of the same gravitational phenomena, by making use…
A general noncommutative-geometric theory of principal bundles is presented. Quantum groups play the role of structure groups. General quantum spaces play the role of base manifolds. A differential calculus on quantum principal bundles is…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We describe a new regularization of quantum field theory on the noncommutative torus by means of one-dimensional matrix models. The construction is based on the Elliott-Evans inductive limit decomposition of the noncommutative torus…
This work introduces topological regularization as a framework for handling ultraviolet divergences in quantum field theory, reinterpreting infinities as topological obstructions at spacetime boundaries. Through geometric compactification…
Quantum real numbers are proposed by performing a quantum deformation of the standard real numbers $\R$. We start with the q-deformed Heisenberg algebra $\cLLq$ which is obtained by the Moyal $\ast$-deformation of the Heisenberg algebra…
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…
We show that a recently introduced generalized scheme of quantum mechanics has connections to Li\'{e}nard and Levinson-Smith classes of nonlinear systems. For the Li\'{e}nard type, which has coefficients of odd and odd symmetry, we…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Characterizing the noise in the set of gate operations that form the building blocks of a quantum computational device is a necessity for assessing the quality of the device. Here, we introduce randomized linear gate set tomography, an…
We introduce a new class of quantum and classical correlation measures by generalizing the reflected entropy to multipartite states. We define the new measures for quantum systems in one spatial dimension. For quantum systems having gravity…
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…
Under ray-optical light transport, the classical ray serves as a linear and local "point query" of light's behaviour. Linearity and locality are crucial to the formulation of sophisticated path tracing and sampling techniques, that enable…