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/9712044 · Physical Review A

Quantum and classical descriptions of a measuring apparatus

Ori Hay, Asher Peres

Published Jul 1, 1998• 29 citations
arXivHTMLPDF

Abstract

A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation and then it must be given a classical description so that the result of the measurement appears as objective reality. Alternatively, the apparatus may always be treated by quantum mechanics and be measured by a second apparatus, which has such a dual description. This article examines whether these two different descriptions are mutually consistent. It is shown that if the dynamical variable used in the first apparatus is represented by an operator of the Weyl-Wigner type (for example, if it is a linear coordinate), then the conversion from quantum to classical terminology does not affect the final result. However, if the first apparatus encodes the measurement in a different type of operator (e.g., the phase operator), the two methods of calculation may give different results.

DOI
10.1103/physreva.58.116

Related papers

Dual Classical and Quantum Descriptions of a Measuring Apparatus

Ori Hay, Asher Peres

The measuring process is the interface of classical and quantum phenomena. A measuring apparatus must be described by quantum mechanics while it interacts with the quantum system under observation. Then, it has to be be given a classical description so that the result of the measurement appears as objective reality. Alternatively, that apparatus may be treated at all times by quantum mechanics. In that case, it never achieves the “objective” status, but it can be measured by a second apparatus which has such a dual description. The question is whether these two different descriptions of the same apparatus are mutually consistent. A detailed analysis leads to the conclusion that not every physical system is a legitimate measuring apparatus. The quantum measurement problem has a satisfactory solution only if the measuring apparatus is properly designed.

Kluwer Academic Publishers eBooks•Dec 19, 2005•0 citations

Measurement and quantum states

Richard Healey

MEASUREMENT INTERACTIONS In the present interpretation terms such as ‘measurement,’ ‘observation,’ ‘find,’ ‘classical,’ and ‘apparatus’ do not appear in the formulation of quantum mechanics. Yet it must of course be true that quantum mechanics can be used to predict features of the results of measurements – in particular their statistics. What is required, then, is an account in quantum mechanical terms of those physical interactions capable of being used to perform measurements of quantum dynamical variables, from which it follows that the predicted probabilities for specified behavior of certain quantum systems in these interactions coincide with what, on a more conventional interpretation, are simply postulated as the quantum mechanical probabilities for various measurement results on a system with a given quantum state. It is necessary to see how this consequence may be derived, not only in order to explicate the Born rules, but also to explain the role of quantum states within the present interpretation. The first step toward the required account is to analyze the nature of an interaction capable of being used to perform a measurement of the value of a quantum dynamical variable in a quantum system. Any such interaction will be called an M -type interaction, whether or not it is in fact used to perform a measurement. The basic characteristic of an M -type interaction is that it establishes a correlation between the initial dynamical state of one quantum system σ (the object system) and the final dynamical state of another quantum system α (the apparatus system).

Cambridge University Press eBooks•Nov 24, 1989•0 citations

Persistence of Information in the Quantum Measurement Problem.

Shantena Augusto Sabbadini

The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus; (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the 'collapse of the wave function') is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e. whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions (1) and (2) to hold when and only when information about measurement results persists. Finally the notion of 'element of reality' introduced by Einstein, Podolsky and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the 'classical' nature of the world we experience.

Physics Essays•Mar 1, 2006•2 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

On the Measurement in Quantum Mechanics: the Consistent Measurement Apparatus

Fabio L. Traversa, Guillermo Albareda

Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the Copenhagen interpretation (i.e., through the collapse of the wavefunction) compared versus a picture in which the system and the measurement apparatus are considered as a whole. We first consider a projective measurement. In this limiting case, the natural requirements of consistency and equivalence between the two pictures lead to the rigorous definition of consistent measuring apparatus: the orthonormal wavefunctions from the Schmidt decomposition of the system plus apparatus must have non-overlapping supports. This result arises from the comparison of the two pictures (otherwise hidden), and while it seems to be an obvious conclusion in the limit of projective measurements, it has some nontrivial implications as one extends its validity to the domain of weak measurements. In this respect, we argue on the existence of two alternative approaches to mathematically constructing a weak measurement protocol. While the two approaches are equivalent from the system's perspective, they do strongly differ from the apparatus point of view, and hence can be only distinguished one from each other in the picture where system and apparatus are considered as a whole. We show that only one of the two mathematical formulations of the weak measurement fulfills the consistent apparatus condition, while the combination of the two gives rise to a generalized weak measurements framework.

arXiv:1602.08818•Feb 29, 2016•0 citations

Interaction between classical and quantum systems: A new approach to quantum measurement. III. Illustration

S. R. Gautam, T. N. Sherry, E. C. G. Sudarshan

Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we examine some simple experiments for the purpose of illustration. The Stern-Gerlach experiment is examined in detail, within our approach, and we see explicitly how the relevant information is transferred to the apparatus variables. We also examine a magnetic interferometer arrangement and a crossed-field arrangement. Consideration of these experiments leads us to the inclusion of an extra procedural step in our approach. This extra step is necessary so that an observer may measure the classical apparatus variables at will after the interaction is completed.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Dec 15, 1979•19 citations
A measuring apparatus is described by quantum mechanics while it interacts with the quantum system under observation and then it must be given a classical description so that the result of the measurement appears as objective reality. Alternatively, the apparatus may always be treated by quantum mechanics and be measured by a second apparatus, which has such a dual description. This article examines whether these two different descriptions are mutually consistent. It is shown that if the dynamical variable used in the first apparatus is represented by an operator of the Weyl-Wigner type (for example, if it is a linear coordinate), then the conversion from quantum to classical terminology does not affect the final result. However, if the first apparatus encodes the measurement in a different type of operator (e.g., the phase operator), the two methods of calculation may give different results.
The measuring process is the interface of classical and quantum phenomena. A measuring apparatus must be described by quantum mechanics while it interacts with the quantum system under observation. Then, it has to be be given a classical description so that the result of the measurement appears as objective reality. Alternatively, that apparatus may be treated at all times by quantum mechanics. In that case, it never achieves the “objective” status, but it can be measured by a second apparatus which has such a dual description. The question is whether these two different descriptions of the same apparatus are mutually consistent. A detailed analysis leads to the conclusion that not every physical system is a legitimate measuring apparatus. The quantum measurement problem has a satisfactory solution only if the measuring apparatus is properly designed.
MEASUREMENT INTERACTIONS In the present interpretation terms such as ‘measurement,’ ‘observation,’ ‘find,’ ‘classical,’ and ‘apparatus’ do not appear in the formulation of quantum mechanics. Yet it must of course be true that quantum mechanics can be used to predict features of the results of measurements – in particular their statistics. What is required, then, is an account in quantum mechanical terms of those physical interactions capable of being used to perform measurements of quantum dynamical variables, from which it follows that the predicted probabilities for specified behavior of certain quantum systems in these interactions coincide with what, on a more conventional interpretation, are simply postulated as the quantum mechanical probabilities for various measurement results on a system with a given quantum state. It is necessary to see how this consequence may be derived, not only in order to explicate the Born rules, but also to explain the role of quantum states within the present interpretation. The first step toward the required account is to analyze the nature of an interaction capable of being used to perform a measurement of the value of a quantum dynamical variable in a quantum system. Any such interaction will be called an M -type interaction, whether or not it is in fact used to perform a measurement. The basic characteristic of an M -type interaction is that it establishes a correlation between the initial dynamical state of one quantum system σ (the object system) and the final dynamical state of another quantum system α (the apparatus system).
The quantum measurement problem has to do with the compatibility of two different prescriptions for the end state of a quantum measurement process: (1) a superposition representing an entangled state of object system and apparatus; (2) a mixture of correlated states of object system and apparatus. The first prescription is a consequence of the linearity of time evolution in quantum mechanics; the second one (corresponding to what is usually called the 'collapse of the wave function') is a basic feature of the axiomatic structure of the theory. This paper proves that the two prescriptions are exactly equivalent whenever information about the results of the measurement persists, i.e. whenever there is some kind of record or trace of the results (all the measurements we are ordinarily concerned with fulfill this requirement). Experimental evidence is cited suggesting that indeed we should expect the equivalence of prescriptions (1) and (2) to hold when and only when information about measurement results persists. Finally the notion of 'element of reality' introduced by Einstein, Podolsky and Rosen is discussed in the context of this description of the measurement process, and a brief remark is offered about the 'classical' nature of the world we experience.
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.
Measurement in quantum mechanics is generally described as an irreversible process that perturbs the wavefunction describing a quantum system. In this work we establish a formal connection between the measurement description within the Copenhagen interpretation (i.e., through the collapse of the wavefunction) compared versus a picture in which the system and the measurement apparatus are considered as a whole. We first consider a projective measurement. In this limiting case, the natural requirements of consistency and equivalence between the two pictures lead to the rigorous definition of consistent measuring apparatus: the orthonormal wavefunctions from the Schmidt decomposition of the system plus apparatus must have non-overlapping supports. This result arises from the comparison of the two pictures (otherwise hidden), and while it seems to be an obvious conclusion in the limit of projective measurements, it has some nontrivial implications as one extends its validity to the domain of weak measurements. In this respect, we argue on the existence of two alternative approaches to mathematically constructing a weak measurement protocol. While the two approaches are equivalent from the system's perspective, they do strongly differ from the apparatus point of view, and hence can be only distinguished one from each other in the picture where system and apparatus are considered as a whole. We show that only one of the two mathematical formulations of the weak measurement fulfills the consistent apparatus condition, while the combination of the two gives rise to a generalized weak measurements framework.
Following the approach to quantum measurement, proposed in an earlier paper, in which the apparatus is treated as a purely classical instrument to be described by the laws of classical mechanics we examine some simple experiments for the purpose of illustration. The Stern-Gerlach experiment is examined in detail, within our approach, and we see explicitly how the relevant information is transferred to the apparatus variables. We also examine a magnetic interferometer arrangement and a crossed-field arrangement. Consideration of these experiments leads us to the inclusion of an extra procedural step in our approach. This extra step is necessary so that an observer may measure the classical apparatus variables at will after the interaction is completed.