Understanding quantum measurement from the solution of dynamical models

  title={Understanding quantum measurement from the solution of dynamical models},
  author={Armen E. Allahverdyan and Roger Balian and Theo M. Nieuwenhuizen},
  journal={Physics Reports},
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… 
Lectures on dynamical models for quantum measurements
In textbooks, ideal quantum measurements are described in terms of the tested system only by the collapse postulate and Born's rule. This level of description offers a rather flexible position for
A sub-ensemble theory of ideal quantum measurement processes
Abstract In order to elucidate the properties currently attributed to ideal measurements, one must explain how the concept of an individual event with a well-defined outcome may emerge from quantum
Simultaneous measurement of two noncommuting quantum variables : Solution of a dynamical model
The possibility of performing simultaneous measurements in quantum mechanics is investigated in the context of the Curie-Weiss model for a projective measurement. Concretely, we consider a spin-1/2
Quantum mechanics via quantum tomography
Starting from a new basic principle inspired by quantum tomography rather than from Born’s rule, this paper gives an elementary, and self-contained deductive approach to quantum mechanics and quantum
Emergences in Quantum Measurement Processes
Abstract Quantum mechanics is acknowledged as the fundamental theory on which the whole fabric of physics is supposed to rely. And yet, the features of quantum measurements, processes that provide
On classical systems and measurements in quantum mechanics
  • E. Deumens
  • Mathematics
    Quantum Studies: Mathematics and Foundations
  • 2019
The recent rigorous derivation of the Born rule from the dynamical law of quantum mechanics Allahverdyan et al. (Phys Rep 525:1–166. https://doi.org/10.1016/j.physrep.2012.11.001, 2013) is taken as
A stochastic model for quantum measurement
We develop a statistical model of microscopic stochastic deviation from classical mechanics based on a stochastic process with a transition probability that is assumed to be given by an exponential
Non-Markovian quantum measurements in the non-invasive limit
In many real quantum systems the measurement is much less invasive than described by the projection postulate. For example, it is performed by weakly coupling a detector for a finite time to the
Collective Dynamics in NMR and Quantum Noise
We introduced an open quantum system model to describe the statistical fluctuations of a spin ensemble in NMR. The model considers an ensemble measurement where the detection coil does not
von Neumann spin measurements with Rashba fields
We show that dynamics in the spin–orbit coupling field simulate the von Neumann measurement of a particle spin. We demonstrate how the measurement influences the spin and coordinate evolution of a


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