Related papers: Asymptotic Spectral Measures, Quantum Mechanics, a…
Various forms of optimality for quantum observables described as normalized positive operator valued measures (POVMs) are studied in this paper. We give characterizations for observables that determine the values of the measured quantity…
We study the action of space-time symmetries on quantum fields in the presence of small departures from locality determined by dynamical gravity. It is shown that, under such relaxation of locality, the symmetries of the theory cannot be…
This work analyzes the asymptotic behaviors of the asymptotically flat solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions for the tensor, vector, and scalar modes are first obtained, written as sums of various…
We consider group-covariant positive operator valued measures (POVMs) on a finite dimensional quantum system. Following Neumark's theorem a POVM can be implemented by an orthogonal measurement on a larger system. Accordingly, our goal is to…
Deformation quantization and geometric quantization on K\"ahler manifolds give the mathematical description of the algebra of quantum observables and the Hilbert spaces respectively, where the later forms a representation of quantum…
Asymptotic symmetries in Carrollian gravitational theories in 3+1 space and time dimensions obtained from "magnetic" and "electric" ultrarelativistic contractions of General Relativity are analyzed. In both cases, parity conditions are…
The construction of a theory of quantum gravity is an outstanding problem that can benefit from better understanding the laws of nature that are expected to hold in regimes currently inaccessible to experiment. Such fundamental laws can be…
The continuous transition from a low resolution quantum nondemolition measurement of light field intensity to a precise measurement of photon number is described using a generalized measurement postulate. In the intermediate regime,…
Both statistics and quantum theory deal with prediction using probability. We will show that there can be established a connection between these two areas. This will at the same time suggest a new, less formalistic way of looking upon basic…
A set of equations is derived from the Boltzmann kinetic equation describing charge transport in semiconductors. The unknowns of these equations depend on the space-time coordinates and the electron energy. The non-parabolic and parabolic…
In this thesis we shall demonstrate that a measurement of position alone in non-commutative space cannot yield complete information about the quantum state of a particle. Indeed, the formalism used entails a description that is non-local in…
Quantum technology is increasingly relying on specialised statistical inference methods for analysing quantum measurement data. This motivates the development of "quantum statistics", a field that is shaping up at the overlap of quantum…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…
We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so…
Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$…
Developments in the foundations of quantum mechanics have identified several attributes and tests associated with the "quantumness" of systems, including entanglement, nonlocality, quantum erasure, Bell test, etc. Here we introduce and…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
The higher-order Stokes phenomenon can emerge in the asymptotic analysis of many problems governed by singular perturbations. Indeed, over the last two decades, the phenomena has appeared in many physical applications, from acoustic and…
We consider the orthogonal polynomials $\{P_{n}(z)\}$ with respect to the measure $|z-a|^{2N c} {\rm e}^{-N |z|^2} \,{\rm d} A(z)$ over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the complex…
In a previous paper we have presented a general scheme for the implementation of symmetric generalized measurements (POVMs) on a quantum computer. This scheme is based on representation theory of groups and methods to decompose matrices…