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Entropy
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Quantum Statistical Decision and Estimation Theory
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Quantum Statistical Decision and Estimation Theory

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Statistical Physics".

Deadline for manuscript submissions: closed (21 June 2021) | Viewed by 6413

Special Issue Editor

Prof. Dr. Stefano Mancini

E-Mail Website
Guest Editor
School of Science and Technology, University of Camerino Via Madonna delle Carceri 9a, 62032 Camerino, Italy
Interests: quantum information theory (including relativistic aspects); dynamical systems and control theory; information geometry

Special Issue Information

Dear colleagues,

Acquiring information about a physical system always involves a decision or an estimation process. Either one must decide which hypothesis best describes the system, or one must estimate the values of parameters characterizing it. Therefore, the study of physical systems can greatly benefit from statistical decision theory, which rests on the application of mathematical statistics tools for optimizing a decision to take following a sample of data. However, down to the quantum level, random phenomena are not subject to the classical probability theory. The formalism designed to describe them accepts the existence of non-commuting random variables and contains the classical theory as a degenerate commutative scheme. In the corresponding interpretation, many problems of the theory of quantum-mechanical measurements become non-commutative analogues of problems of statistical decision theory.

With the advent of quantum information theory, the fields of statistical decision and quantum measurement become cross-fertilized. The aim of this Special Issue is to put forward up-to-date achievements and to provide surveys on topics at this border. The special issue is partly inspired by the project Quartet (Quantum readout techniques and technologies) funded by EU under the Future and Emerging Technologies programme.

Prof. Dr. Stefano Mancini
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • parametric statistical models
  • hypothesis testing
  • parameter estimation
  • statistical sampling
  • large deviations
  • error exponents
  • loss functions
  • Bayesian inference and Bayesian decision
  • entropy estimation
  • Fisher information
  • channel discrimination
  • nonparametric statistical models
  • density estimation

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Published Papers (2 papers)

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Research

30 pages, 460 KiB  
Article
Differential Geometric Aspects of Parametric Estimation Theory for States on Finite-Dimensional C∗-Algebras
by Florio M. Ciaglia, Jürgen Jost and Lorenz Schwachhöfer
Entropy 2020, 22(11), 1332; https://doi.org/10.3390/e22111332 - 23 Nov 2020
Cited by 8 | Viewed by 2999
Abstract
A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with [...] Read more.
A geometrical formulation of estimation theory for finite-dimensional C∗-algebras is presented. This formulation allows to deal with the classical and quantum case in a single, unifying mathematical framework. The derivation of the Cramer–Rao and Helstrom bounds for parametric statistical models with discrete and finite outcome spaces is presented. Full article
(This article belongs to the Special Issue Quantum Statistical Decision and Estimation Theory)
16 pages, 8519 KiB  
Article
On the Quantumness of Multiparameter Estimation Problems for Qubit Systems
by Sholeh Razavian, Matteo G. A. Paris and Marco G. Genoni
Entropy 2020, 22(11), 1197; https://doi.org/10.3390/e22111197 - 23 Oct 2020
Cited by 23 | Viewed by 2675
Abstract
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. [...] Read more.
The estimation of more than one parameter in quantum mechanics is a fundamental problem with relevant practical applications. In fact, the ultimate limits in the achievable estimation precision are ultimately linked with the non-commutativity of different observables, a peculiar property of quantum mechanics. We here consider several estimation problems for qubit systems and evaluate the corresponding quantumnessR, a measure that has been recently introduced in order to quantify how incompatible the parameters to be estimated are. In particular, R is an upper bound for the renormalized difference between the (asymptotically achievable) Holevo bound and the SLD Cramér-Rao bound (i.e., the matrix generalization of the single-parameter quantum Cramér-Rao bound). For all the estimation problems considered, we evaluate the quantumness R and, in order to better understand its usefulness in characterizing a multiparameter quantum statistical model, we compare it with the renormalized difference between the Holevo and the SLD-bound. Our results give evidence that R is a useful quantity to characterize multiparameter estimation problems, as for several quantum statistical model, it is equal to the difference between the bounds and, in general, their behavior qualitatively coincide. On the other hand, we also find evidence that, for certain quantum statistical models, the bound is not in tight, and thus R may overestimate the degree of quantum incompatibility between parameters. Full article
(This article belongs to the Special Issue Quantum Statistical Decision and Estimation Theory)
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