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Entropy
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Quantum Measurements and Quantum Metrology
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Quantum Measurements and Quantum Metrology

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

Deadline for manuscript submissions: 30 November 2026 | Viewed by 1826

Special Issue Editor

Prof. Dr. János A. Bergou

E-Mail Website
Guest Editor
Department of Physics and Astronomy, Hunter College of the City University of New York, New York, NY, USA
Interests: quantum optics; laser physics; cavity QED and micromasers; nonlinear optics; resonance fluorescence; squeezing and non-classical radiation; quantum information and quantum computing; quantum measurement theory

Special Issue Information

Dear Colleagues,

Quantum measurements and quantum sensing are two rapidly evolving and closely related areas of quantum physics that are currently at the forefront of research. Their scope ranges from the very foundations, establishing and testing fundamental limits on the resolution of quantum measurements, to widespread applications, not least in the area of quantum information processing, quantum communication, and quantum algorithms. On the measurement front, POVMs and weak measurements have become part of the information processing toolbox. For example, SIC POVMs have found widespread application in quantum state tomography. In the area of sensing and metrology, the quantum Fisher information, as well as the related Cramér–Rao bound, is employed to estimate the ultimate precision in quantum metrology. The aim of this Special Issue is to document the maturity of the field and, at the same time, to advance it further. This Special Issue welcomes contributions from experimentalists and theorists in these broadly defined areas. Manuscripts can be in the form of full-length research articles, reviews, or short communications. The topics to be addressed in this Special Issue include, but are not limited to, the following:

  • Quantum measurements;
  • Fundamental limits;
  • POVMs and weak measurements;
  • Continuous variable systems;
  • Quantum state tomography;
  • Quantum sensing and metrology;
  • Quantum Fisher information;
  • The Cramer–Rao bound;
  • Sensor arrays.

Prof. Dr. János A. Bergou
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 250 words) can be sent to the Editorial Office for assessment.

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

  • quantum measurements
  • quantum sensing
  • quantum metrology
  • quantum Fisher information
  • quantum state tomography
  • positive operator-valued measure (POVM)
  • Cramer–Rao bound

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (2 papers)

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Research

19 pages, 9119 KB  
Article
Sampling Quantum States with Inequality Constraints
by Weijun Li, Rui Han, Jiangwei Shang, Hui Khoon Ng and Berthold-Georg Englert
Entropy 2026, 28(6), 614; https://doi.org/10.3390/e28060614 - 29 May 2026
Viewed by 170
Abstract
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one already encounters when working with a few qubits, the quantum state space has a very [...] Read more.
Random samples of quantum states with specific properties are useful for various applications, such as Monte Carlo integration over the state space. In the high-dimensional situations that one already encounters when working with a few qubits, the quantum state space has a very complicated boundary, and it is challenging to incorporate the specific properties into the sampling algorithm. In this paper, we present the Sequentially Constrained Monte Carlo (SCMC) algorithm as a practical and versatile method for sampling quantum states in accordance with properties that can be stated as inequalities. We apply the SCMC algorithm to the generation of samples of bound entangled states; for example, we obtain nearly ten thousand bound, entangled, two-qutrit states in a few minutes, compared with less than ten such states per day from independence sampling in our implementation. In the second application, we draw samples of high-dimensional quantum states from a narrowly peaked target distribution and observe, for the system sizes investigated, that SCMC sampling remains computationally manageable as the dimensions grow. In yet another application, the SCMC algorithm produces uniformly distributed quantum states in regions bounded by values of the problem-specific target distribution; such samples are needed when estimating parameters from the probabilistic data acquired in quantum experiments. Full article
(This article belongs to the Special Issue Quantum Measurements and Quantum Metrology)
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21 pages, 991 KB  
Article
Hybrid Cramér-Rao Bound for Quantum Bayes Point Estimation with Nuisance Parameters
by Jianchao Zhang and Jun Suzuki
Entropy 2025, 27(12), 1184; https://doi.org/10.3390/e27121184 - 21 Nov 2025
Viewed by 1078
Abstract
We develop a hybrid framework for quantum parameter estimation in the presence of nuisance parameters. In this scheme, the parameters of interest are treated as fixed non-random parameters while nuisance parameters are integrated out with respect to a prior (random parameters). Within this [...] Read more.
We develop a hybrid framework for quantum parameter estimation in the presence of nuisance parameters. In this scheme, the parameters of interest are treated as fixed non-random parameters while nuisance parameters are integrated out with respect to a prior (random parameters). Within this setting, we introduce the hybrid partial quantum Fisher information matrix (hpQFIM), defined by prior-averaging the nuisance block of the QFIM and taking a Schur complement, and derive a corresponding Cramér–Rao-type lower bound on the hybrid risk. We establish the structural properties of the hpQFIM, including inequalities that bracket it between computationally tractable approximations, as well as limiting behaviors under extreme priors. Operationally, the hybrid approach improves over pure point estimation since the optimal measurement for the parameters of interest depends only on the prior distribution of the nuisance, rather than on its unknown value. We illustrate the framework with analytically solvable qubit models and numerical examples, clarifying how partial prior information on nuisance variables can be systematically exploited in quantum metrology. Full article
(This article belongs to the Special Issue Quantum Measurements and Quantum Metrology)
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