Related papers: Informational completeness of continuous-variable …
The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…
We study holomorphic foliations with an affine homogeneous transverse structure. We give a friendly characterization of the case of transversely affine foliations in terms of matrix valued pairs of differential forms. This leads naturally…
Quantum tomography is a procedure to determine the quantum state of a physical system, or equivalently, to estimate the expectation value of any operator. It consists in appropriately averaging the outcomes of the measurement results of…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
Accessible information, which is a basic quantity in quantum information theory, is computed for a general quantum Gaussian ensemble under certain "threshold condition". It is shown that the maximizing measurement is Gaussian, constituting…
Using only elementary calculus we prove that the balanced homodyne detector measures the quadrature phase amplitude of a signal. More precisely, after the measurement of photon numbers $l$, the collapse of the composite state of a strong…
We consider the stationary measure of the dissipative dynamical system in a finite volume. A finite dissipation, however small, generally makes the measure singular, while at zero dissipation the measure is constant. Thus dissipative part…
I review progress made in solving gauge theories such as collinear quantum chromodynamics using light-cone Hamiltonian methods. I also show how the light-cone Fock expansion for hadron wavefunctions can be used to compute operator matrix…
Travelling modes of single-photon-added coherent states (SPACS) are characterized via optical homodyne tomography. Given a set of experimentally measured quadrature distributions, we estimate parameters of the state and also extract…
We consider Non Autonomous Conformal Iterative Function Systems (NACIFS) and their limit set. Our main concern is harmonic measure and its dimensions : Hausdorff and Packing. We prove that this two dimensions are continuous under…
We prove that a homomorphism $h:X\to Y$ from a (locally compact) Cech-complete topological group $X$ to a topological group $Y$ is continuous if and only if $h$ is Borel-measurable if and only if $h$ is universally measurable (if and only…
We show that the full statistics of the two detectors outputs in a balanced homodyne detection setup involving a local oscillator in an ideal coherent state is experimentally accessible despite the excess noise existing in actual laser…
The paper gives first quantitative estimates on the modulus of continuity of the spectral measure for weak mixing suspension flows over substitution automorphisms, which yield information about the "fractal" structure of these measures. The…
For a domain $G$ in the one-point compactification $\overline{\mathbb{R}}^n = \mathbb{R}^n \cup \{ \infty\}$ of $\mathbb{R}^n, n \ge 2$, we characterize the completeness of the modulus metric $\mu_G$ in terms of a potential-theoretic…
Major revision of the thermodynamics is made in order to provide rigorous fundament for functional diversity of holistic type. It turns out that the new approach ensures reproducibility of the information as well.
We suggest and demonstrate a tomographic method to fully characterize homodyne detectors at the quantum level. The operator measure associated with the detector is expanded in the quadrature basis and probed with a set of coherent states.…
We establish a criterion for the completeness of an exponential system in the spaces of functions continuous on a convex compact set and holomorphic in the interior of this compact set, as well as in the spaces of holomorphic functions in…
We perform a quantum information analysis for multi-mode Gaussian approximate position measurements, underlying noisy homodyning in quantum optics. The "Gaussian maximizer" property is established for the entropy reduction of these…
Generalized symmetric informationally complete (SIC) measurements are SIC measurements that are not necessarily rank one. They are interesting originally because of their connection with rank-one SICs. Here we reveal several merits of…
We study the persistent homology of both functional data on compact topological spaces and structural data presented as compact metric measure spaces. One of our goals is to define persistent homology so as to capture primarily properties…