# Understanding quantum measurement from the solution of dynamical models

@article{Allahverdyan2013UnderstandingQM, title={Understanding quantum measurement from the solution of dynamical models}, author={Armen E. Allahverdyan and Roger Balian and Theo M. Nieuwenhuizen}, journal={Physics Reports}, year={2013}, volume={525}, pages={1-166} }

Abstract The quantum measurement problem, to wit, understanding why a unique outcome is obtained in each individual experiment, is currently tackled by solving models. After an introduction we review the many dynamical models proposed over the years for elucidating quantum measurements. The approaches range from standard quantum theory, relying for instance on quantum statistical mechanics or on decoherence, to quantum–classical methods, to consistent histories and to modifications of the…

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## References

SHOWING 1-10 OF 538 REFERENCES

Quantum measurement as a driven phase transition: An exactly solvable model

- Physics
- 2001

A model of quantum measurement is proposed, which aims to describe statistical mechanical aspects of this phenomenon, starting from a purely Hamiltonian formulation. The macroscopic measurement…

Curie-Weiss model of the quantum measurement process

- Physics, Mathematics
- 2002

A Hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-½, whose z-component is measured through coupling with an apparatus A…

Collapse of the Quantum Wavefunction

- Physics
- 2008

Physics Department, Norwegian University of Science and Technology(Dated: September 9, 2008)We show using a realistic Hamiltonian-type model that deﬁnite outcomes of quantum measure-ments may emerge…

Quantum approach to coupling classical and quantum dynamics

- Physics
- 2000

We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, such as evolutions that do…

Dynamics of a quantum measurement

- Physics, Mathematics
- 2004

We work out an exactly solvable Hamiltonian model which retains all the features of realistic quantum measurements. In order to use an interaction process involving a system and an apparatus as a…

Simultaneous measurement of non-commuting observables

- Physics
- 2010

Abstract A dynamical model of a quantum measurement process is introduced, where the tested system S, a spin 1 2 , is simultaneously coupled with two apparatuses A and A ′ . Alone, A would measure…

On the mathematical Structure of Quantum Measurement Theory

- Physics, Mathematics
- 2005

We show that the key problems of quantum measurement theory, namely the reduction of the wave packet of a microsystem and the specification of its quantum state by a macroscopic measuring instrument,…

Emergence of quantum mechanics from classical statistics

- Physics, Mathematics
- 2009

The conceptual setting of quantum mechanics is subject to an ongoing debate from its beginnings until now. The consequences of the apparent differences between quantum statistics and classical…

Can the Quantum Measurement Problem be Resolved within the Framework of Schroedinger Dynamics and Quantum Probability

- Physics, Mathematics
- 2005

We provide an affirmative answer to the question posed in the title. Our argument is based on a treatment of the Schroedinger dynamics of the composite, Sc, of a quantum microsystem, S, and a…

Pointer states via Decoherence in a Quantum Measurement

- Physics
- 1999

We consider the interaction of a quantum system (spin-1/2) with a macroscopic quantum apparatus (harmonic oscillator) which in turn is coupled to a bath of harmonic oscillators. Exact solutions of…