Dynamic reduction to stationary states in quantum measurements

Abstract

Background and Objectives: According to the quantum theory, a change in the states of a quantum system occurs either by continuous deterministic evolution or by almost instantaneous probabilistic projection into its own stationary states as a result of interaction with a classical measuring device. In the theory of quantum measurement, such projection can be carried out both at the beginning and at the end of the measuring chain. In the latter case, а paradoxical theoretical conclusion may arise that selection of the state to which reduction leads can only occur in the mind of the observer. This article proposes a model of measurements in which selection occurs dynamically in the quantum system itself being measured. Methods: A dynamic model of wave function reduction under quantum measurement is proposed. The reduction to a stationary state as a gate process was simulated, including evolution according to the Schrodinger equation and periodic zeroing of the imaginary part of the wave function. Conclusion: Modeling of dynamic reduction to various stationary states of a particle in a potential box and an oscillator has shown that the reduction occurs on a time scale of the order of several tens of the periods of oscillation of the ground state. Moreover, within the framework of this measurement model, the Zeno effect of freezing а resonant quantum transition has been confirmed. If a state decays, measurement cannot prevent decay, but it can slow it down. It is important that during dynamic measurement, the selection of the measured state is present in the measurement itself and leads to a result recorded by the device before the observer. We can also say that the Schrodinger equation is compatible with procedures for reduction of quantum states.

Keywords

• quantum measurement
• reduction of the wave function
• collapse of the wave function
• projective postulate
• quantum zeno effect