arXiv subjects

Roberto Beneduci

Publications and source records attributed to Roberto Beneduci.

13 recordsLinked to original sources

arXiv2023

Forest fire spreading: a nonlinear stochastic model continuous in space and time

Forest fire spreading is a complex phenomenon characterized by a stochastic behavior. Nowadays, the enormous quantity of georeferenced data and the availability of powerful techniques for their analysis can provide a very careful picture of forest fires opening the way to more realistic models. We propose a stochastic spreading model continuous in space and time that is able to use such data in their full power. The state of the forest fire is described by the subprobability densities of the green trees and of the trees on fire that can be estimated thanks to data coming from satellites and earth detectors. The fire dynamics is encoded into a density probability kernel which can take into account wind conditions, land slope, spotting phenomena and so on, bringing to a system of integro-differential equations for the probability densities. Existence and uniqueness of the solutions is proved by using Banach's fixed point theorem. The asymptotic behavior of the model is analyzed as well. Stochastic models based on cellular automata can be considered as particular cases of the present model from which they can be derived by space and/or time discretization. Suggesting a particular structure for the kernel, we obtain numerical simulations of the fire spreading under different conditions. For example, in the case of a forest fire evolving towards a river, the simulations show that the probability density of the trees on fire is different from zero beyond the river due to the spotting phenomenon. Firefighters interventions and weather changes can be easily introduced into the model.

q-bio.PE↗

arXiv2022

Incompatibility of effects in general probabilistic models

We give a necessary and sufficient condition for the incompatibility of a pair of effects in a general probabilistic model in which the state space is a total convex space, which can be obtained by minimising a real parameter. This has an interpretation in terms of the least noise that must be included to make the given pair compatible.

quant-ph↗

arXiv2021

Quantum Description of Angles in the Plane

The real plane with its set of orientations or angles in $[0,\pi)$ is the simplest non trivial example of a (projective) Hilbert space and provides nice illustrations of quantum formalism. We present some of them, namely covariant integral quantization, linear polarisation of light as a quantum measurement, interpretation of entanglement leading to the violation of Bell inequalities, and spin one-half coherent states viewed as two entangled angles.

quant-ph↗

arXiv2021

Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light

We investigate two aspects of the elementary example of POVMs on the Euclidean plane, namely their status as quantum observables and their role as quantizers in the integral quantization procedure. The compatibility of POVMs in the ensuing quantum formalism is discussed, and a Naimark dilation is found for the quantum operators. The relation with Toeplitz quantization is explained. A physical situation is discussed, where we describe the linear polarization of the light with the use of Stokes parameters. In particular, the case of sequential measurements in a real bidimensional Hilbert space is addressed. An interpretation of the Stokes parameters in the framework of unsharp or fuzzy observables is given. Finally, a necessary condition for the compatibility of two dichotomic fuzzy observables which provides a condition for the approximate joint measurement of two incompatible sharp observables is found.

quant-ph↗

arXiv2018

Positive Operator Valued Measures and Feller Markov Kernels

A Positive Operator Valued Measure (POVM) is a map $F:\mathcal{B}(X)\to\mathcal{L}_s^+(\mathcal{H})$ from the Borel $σ$-algebra of a topological space $X$ to the space of positive self-adjoint operators on a Hilbert space $\mathcal{H}$. We assume $X$ to be Hausdorff, locally compact and second countable and prove that a POVM $F$ is commutative if and only if it is the smearing of a spectral measure $E$ by means of a Feller Markov kernel. Moreover, we prove that the smearing can be realized by means of a strong Feller Markov kernel if and only if $F$ is uniformly continuous. Finally, we prove that a POVM which is norm bounded by a finite measure $ν$ admits a strong Feller Markov kernel. That provides a characterization of the smearing which connects a commutative POVM $F$ to a spectral measure $E$ and is relevant both from the mathematical and the physical viewpoint since smearings of spectral measures form a large and very relevant subclass of POVMs: they are paradigmatic for the modeling of certain standard forms of noise in quantum measurements, they provide optimal approximators as marginals in joint measurements of incompatible observables \cite{Busch}, they are important for a range of quantum information processing protocols, where classical post-processing plays a role \cite{Heinosaari}. The mathematical and physical relevance of the results is discussed and particular emphasis is given to the connections between the Markov kernel and the imprecision of the measurement process.

math.FA↗

arXiv2015

Joint measurability through Naimark's theorem

We use Naimark's dilation theorem in order to characterize the joint measurability of two POVMs. Then, we analyze the joint measurability of two commutative POVMs $F_1$ and $F_2$ which are the smearing of two self-adjoint operators $A_1$ and $A_2$ respectively. We prove that the compatibility of $F_1$ and $F_2$ is connected to the existence of two compatible self-adjoint dilations $A_1^+$ and $A_2^+$ of $A_1$ and $A_2$ respectively. As a corollary we prove that each couple of self-adjoint operators can be dilated to a couple of compatible self-adjoint operators. Next, we analyze the joint measurability of the unsharp position and momentum observables and show that it provides a master example of the scheme we propose. Finally, we give a sufficient condition for the compatibility of two effects.

quant-ph↗

arXiv2013

On the Unavoidability of the Interpretations of Quantum Mechanics

Recently, the presence in the literature (also recent) of voluminous discussions about the interpretation of quantum mechanics has been labelled as scandalous. We claim that a weak point of the debate which hosted such a conclusion is a lack of a definition of the term "interpretation". In the present note, we would "like to make precise" that meaning and to show how such a clarification is necessary in order to avoid misunderstandings.

physics.hist-ph↗

arXiv2013

An operational link between MUBs and SICs

We exhibit an operational connection between mutually unbiased bases and symmetric infomationally complete positive operator-valued measures. Assuming that the latter exists, we show that there is a strong link between these two structures in all prime power dimensions. We also demonstrate that a similar link cannot exists in dimension 6.

quant-ph↗

arXiv2013

Semispectral Measures and Feller markov Kernels

We give a characterization of commutative semispectral measures by means of Feller and Strong Feller Markov kernels. In particular: {itemize} we show that a semispectral measure $F$ is commutative if and only if there exist a self-adjoint operator $A$ and a Markov kernel $μ_{(\cdot)}(\cdot):Γ\times\mathcal{B}(\mathbb{R})\to[0,1]$, $Γ\subsetσ(A)$, $E(Γ)=\mathbf{1}$, such that $$F(Δ)=\int_Γμ_Δ(λ)\,dE_λ,$$ \noindent and $μ_{(Δ)}$ is continuous for each $Δ\in R$ where, $R\subset\mathcal{B}(\mathbb{R})$ is a ring which generates the Borel $σ$-algebra of the reals $\mathcal{B}(\mathbb{R})$. Moreover, $μ_{(\cdot)}(\cdot)$ is a Feller Markov kernel and separates the points of $Γ$. we prove that $F$ admits a strong Feller Markov kernel $μ_{(\cdot)}(\cdot)$, if and only if $F$ is uniformly continuous. Finally, we prove that if $F$ is absolutely continuous with respect to a regular finite measure $ν$ then, it admits a strong Feller Markov kernel. {itemize} The mathematical and physical relevance of the results is discussed giving a particular emphasis to the connections between $μ$ and the imprecision of the measurement apparatus.

math.FA↗

arXiv2013

Uniform continuity of POVMs

Recently a characterization of uniformly continuous POVMs and a necessary condition for a uniformly continuous POVM $F$ to have the norm-1 property have been provided. Moreover it was proved that in the commutative case, uniform continuity corresponds to the existence of a Feller Markov kernel. We apply such results to the analysis of some relevant physical examples; i.e., the phase space localization observables, the unsharp phase observable and the unsharp number observable of which we study the uniform continuity, the norm-1 property and the existence of a Feller Markov kernel.

quant-ph↗

arXiv2012

A note on the Relationship between Localization and Norm-1 Property

The paper focuses on the problem of localization in quantum mechanics. It is well known that it is not possible to define a localization observable for the photon by means of projection valued measures. Conversely, that is possible by using positive operator valued measures. On the other hand, projection valued measures imply a kind of localization which is stronger than the one implied by positive operator valued measures. It has been claimed that the norm-1 property would in some sense reduce the gap between the two kind of localizations. We give a necessary condition for the norm-1 property and show that it is not satisfied by several important localization observables.

quant-ph↗

arXiv2010

Neumark Operators and Sharp Reconstructions, the finite dimensional case

A commutative POV measure $F$ with real spectrum is characterized by the existence of a PV measure $E$ (the sharp reconstruction of $F$) with real spectrum such that $F$ can be interpreted as a randomization of $E$. This paper focuses on the relationships between this characterization of commutative POV measures and Neumark's extension theorem. In particular, we show that in the finite dimensional case there exists a relation between the Neumark operator corresponding to the extension of $F$ and the sharp reconstruction of $F$. The relevance of this result to the theory of non-ideal quantum measurement and to the definition of unsharpness is analyzed.

math-ph↗

arXiv2001

Individual consistency of 2-events quantum histories

We introduce a new notion of consistency for 2-events quantum histories, based on the concept of mirror projection. Contrary to all notions of consistency so far introduced, our consistency, named self-decoherence, is an individual property, i.e., it can be attributed to every single sample of the physical system. Furthermore, self-decoherence forbids contrary inferences.

quant-ph↗