Dynamical Model of Quantum Measurement

Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the $z$ -component of a spin- $\frac{1}{2}$ ( $s_z=\pm\frac{1}{2}$ ) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin- $\frac{1}{2}$ case are cast in general notation. The dynamics of the measurement of the $z$ -component of a spin-1 ( $s_z=0,\pm 1$ ) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the $z$-component of a spin-$\frac{1}{2}$ ($s_z=\pm\frac{1}{2}$) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin-$\frac{1}{2}$ case are cast in general notation. The dynamics of the measurement of the $z$-component of a spin-1 ($s_z=0,\pm 1$) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.

quant-pharXiv:2603.07153Frontiers in Quantum Science and TechnologyMar 10, 20260 citations

Dynamics of a quantum measurement

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

arXiv:quant-ph/0412045Physica E Low-dimensional Systems and NanostructuresJul 13, 20058 citations

MEASUREMENTS IN QUANTUM MECHANICS AND von NEUMANN’s MODEL

Pier A. Mello, Lars M. Johansen, Moises Martinez-Mares +1 more

Many textbooks on Quantum Mechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in Quantum Mechanics, including the measuring instrument in the formalism.In this article we apply von Neumann’s model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge.We also investigate the more complex, intriguing and fundamental problem of two successive measurements in Quantum Mechanics, extending von Neumann’s model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.Many textbooks on Quantum Mechanics are not very precise as to the meaning of making a measurement: as a consequence, they frequently make assertions which are not based on a dynamical description of the measurement process. A model proposed by von Neumann allows a dynamical description of measurement in Quantum Mechanics, including the measuring instrument in the formalism.In this article we apply von Neumann’s model to illustrate the measurement of an observable by means of a measuring instrument and show how various results, which are sometimens postulated without a dynamical basis, actually emerge.We also investigate the more complex, intriguing and fundamental problem of two successive measurements in Quantum Mechanics, extending von Neumann’s model to two measuring instruments. We present a description which allows obtaining, in a unified way, various results that have been given in the literature.

AIP conference proceedingsJan 1, 20103 citations

Understanding quantum measurement from the solution of dynamical models

ARMEN E. ALLAHVERDYAN, Roger Balian, Theo M. Nieuwenhuizen

arXiv:1107.2138Physics ReportsNov 14, 2012239 citations

Quantum measurement and dynamical maps

E. C. G. Sudarshan

Jan 1, 19856 citations

Quantum measurement is a dynamical process of an apparatus coupled to a test system. Ideal measurement of the

z

-component of a spin-

\frac{1}{2}

(

s_z=\pm\frac{1}{2}

) has been modeled by the Curie-Weiss model for quantum measurement. Recently, the model was generalized to higher spin and the thermodynamics was solved. Here the dynamics is considered. To this end, the dynamics for spin-

\frac{1}{2}

case are cast in general notation. The dynamics of the measurement of the

z

-component of a spin-1 (

s_z=0,\pm 1

) are solved in detail and evaluated numerically. Energy costs of the measurement, which are macroscopic, are evaluated. Generalization to higher spin is straightforward.