Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0306120 · Physical Review A

Entangling quantum measurements and their properties

B. A. Grishanin, Victor N. Zadkov

Published Aug 20, 2003• 8 citations
arXivHTMLPDF

Abstract

We study the mathematical structure of superoperators describing quantum measurements, including the entangling measurement---the generalization of the standard quantum measurement that results in entanglement between the measurable system and apparatus. It is shown that the coherent information can be effectively used for the analysis of such entangling measurements whose possible applications are discussed as well.

DOI
10.1103/physreva.68.022309

Related papers

Entangling quantum measurements

B. A. Grishanin, Victor N. Zadkov

The concept of an entangling measurement as the most general form of ideal quantum measurement is introduced. The mathematical definition of an entangling measurement is given in the form of a superoperator transformation, which projects the initial states of an object-apparatus system on the corresponding entangled states appearing after a measurement. The mathematical properties of the superoperator of an entangling measurement are considered. The spectrum of superoperator eigenstates is studied analytically on the example of a two-level system. The algebraic relation ℳ 2 =ℳ AM between the superoperators of entangling and standard measurements is ascertained. The coherent information obtained in the course of measurement is analyzed and the relevant potentialities of entangling measurements are discussed.

Optics and Spectroscopy•Jun 8, 2004•3 citations

On the general quantum theory of measurement

Arthur I. Fine

We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.

Mathematical Proceedings of the Cambridge Philosophical Society•Jan 1, 1969•29 citations

Correlation properties of quantum measurements

Paul Busch, Pekka J. Lahti

The kind of information provided by a measurement is determined in terms of the correlation established between observables of the apparatus and the measured system. Using the framework of quantum measurement theory, necessary and sufficient conditions for a measurement interaction to produce strong correlations are given and are found to be related to properties of the final object and apparatus states. These general results are illustrated with reference to the standard model of the quantum theory measurement.

arXiv:quant-ph/9603016•Journal of Mathematical Physics•Jun 1, 1996•13 citations

Coherent and compatible information: a basis for information analysis of quantum systems

B. A. Grishanin, Victor N. Zadkov

Relevance of key quantum information measures for analysis of quantum systems is discussed. It is argued that possible ways of measuring quantum information are based on compatibility/incompatibility of the quantum states of a quantum system, resulting in the coherent information and introduced her the compatible information measures, respectively. A sketch of an information optimization of a quantum experimental setup is proposed.

arXiv:quant-ph/0108035•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Apr 3, 2002•2 citations

Entanglement preventing measurements on simple quantum systems

Paul Bracken

The nature and role of the measuring apparatus in the process of measurement in quantum mechanics is discussed. In the Schrödinger picture, the measurement generates an entanglement between the eigenstates of the observable and the states of the apparatus, which becomes part of the overall system. It is shown that with respect to some small systems, this entanglement can be prevented, and that it should be possible to carry out such experiments.

Molecular Physics•Aug 10, 2005•0 citations

Generalized Exact Fractional Quantum Information Model with Memory Effects

Abdelmalek Bouzenada, Allan R. P. Moreira

In this paper, we analyze quantum information measures in fractional quantum mechanics using the Riemann-Liouville derivative formalism adopted here. In this case, we initially reconsider the conventional definitions of Shannon entropy and Fisher information, subsequently extending them to fractional quantum systems described by nonlocal differential operator frameworks adopted. Within this generalized formulation, fractional expressions of Shannon entropy and Fisher information are constructed and their mathematical structures examined thoroughly. Also, the formalism is then applied to the quantum harmonic oscillator, yielding explicit analytical expressions derived as functions of the fractional parameter therein. The obtained results demonstrate that fractional derivatives alter the localization properties of probability densities and generate nontrivial variations in information content and sensitivity across system behavior. In this context, the fractional parameter plays a central role in controlling deviations from the standard quantum information measures framework. Also, the study establishes a consistent framework for describing information-theoretic properties of quantum systems governed by nonlocal dynamics.

quant-pharXiv:2606.13525•Jun 12, 2026•0 citations
We study the mathematical structure of superoperators describing quantum measurements, including the entangling measurement---the generalization of the standard quantum measurement that results in entanglement between the measurable system and apparatus. It is shown that the coherent information can be effectively used for the analysis of such entangling measurements whose possible applications are discussed as well.
The concept of an entangling measurement as the most general form of ideal quantum measurement is introduced. The mathematical definition of an entangling measurement is given in the form of a superoperator transformation, which projects the initial states of an object-apparatus system on the corresponding entangled states appearing after a measurement. The mathematical properties of the superoperator of an entangling measurement are considered. The spectrum of superoperator eigenstates is studied analytically on the example of a two-level system. The algebraic relation ℳ 2 =ℳ AM between the superoperators of entangling and standard measurements is ascertained. The coherent information obtained in the course of measurement is analyzed and the relevant potentialities of entangling measurements are discussed.
We use the term ‘measurement’ to refer to the interaction between an object and an apparatus on the basis of which information concerning the initial state of the object may be obtained from information on the resulting state of the apparatus. The quantum theory of measurement is a quantum theoretic investigation of such interactions in order to analyse the correlations between object and apparatus that measurement must establish. Although there is a sizeable literature on quantum measurements there appear to be just two sorts of interactions that have been employed. There are the ‘disturbing’ interactions consistent with the analysis of Landau and Peierls (8) as developed by Pauli (11) and by Landau and Lifshitz (7), and there are the ‘non-disturbing’ interactions explicitly set out by von Neumann ((10), chs. 5, 6), and that dominate the literature. In this paper we shall investigate the most general types of interactions that could possibly constitute measurements and provide a precise mathematical characterization (section 2). We shall then examine an interesting subclass, corresponding to Landau's ideas, that contains both of the above sorts of measurements (section 3). Finally, we shall discuss von Neumann measurements explicitly and explore the purported limitations suggested by Wigner(12) and Araki and Yanase (2). We hope, in this way, to provide a comprehensive basis for discussions of quantum measurements.
The kind of information provided by a measurement is determined in terms of the correlation established between observables of the apparatus and the measured system. Using the framework of quantum measurement theory, necessary and sufficient conditions for a measurement interaction to produce strong correlations are given and are found to be related to properties of the final object and apparatus states. These general results are illustrated with reference to the standard model of the quantum theory measurement.
In this paper, we analyze quantum information measures in fractional quantum mechanics using the Riemann-Liouville derivative formalism adopted here. In this case, we initially reconsider the conventional definitions of Shannon entropy and Fisher information, subsequently extending them to fractional quantum systems described by nonlocal differential operator frameworks adopted. Within this generalized formulation, fractional expressions of Shannon entropy and Fisher information are constructed and their mathematical structures examined thoroughly. Also, the formalism is then applied to the quantum harmonic oscillator, yielding explicit analytical expressions derived as functions of the fractional parameter therein. The obtained results demonstrate that fractional derivatives alter the localization properties of probability densities and generate nontrivial variations in information content and sensitivity across system behavior. In this context, the fractional parameter plays a central role in controlling deviations from the standard quantum information measures framework. Also, the study establishes a consistent framework for describing information-theoretic properties of quantum systems governed by nonlocal dynamics.