Quantum Dynamical Approach of Wavefunction Collapse in Measurement Process and Its Application to Quantum Zeno Effect

TL;DR

This paper presents a dynamical approach to wavefunction collapse in quantum measurement, demonstrating how off-diagonal density matrix elements vanish in the macroscopic limit and applying this to analyze the quantum Zeno effect and decoherence.

Contribution

It introduces a generalized dynamical model for wavefunction collapse, extending existing models to many-level systems and connecting decoherence with quantum Zeno effect observations.

Findings

Off-diagonal elements vanish in the macroscopic limit with large particle number N.

Quantum information entropy quantifies decoherence and is exactly computed for two-level systems.

The approach explains recent quantum Zeno effect experiments through entropy transition analysis.

Abstract

The systematical studies on the dynamical approach of wavefunction collapse in quantum measurement are reported in this paper based on the Hepp-Coleman's model and its generalizations. Under certain physically reasonable conditions, which are easily satisfied by the practical problems, it is shown that the off-diagonal elements of the reduced density matrix vanish in quantum mechanical evolution process in the macroscopic limit with a very large particle number N. Various examples with detector made up of oscillators of different spectrum distribution are used to illustrate this observations . With the two-level system as an explicit illustration, the quantum information entropy is exactly obtained to quantitatively describe the degree of decoherence for the so-called partial coherence caused by detector. The entropy for the case with many levels is computed based on perturbation method in the limits with very large and very small N. As an application of this general approach for quantum measurement, a dynamical realization of the quantum Zeno effect are present to analyse its recent testing experiment in connection with a description of transition in quantum information entropy. Finally, the Cini's model for the correlation between the states of the measured system and the detector is generalized for the case with many energy-level.