Time-dependent pointer states and determination of the preferred basis of measurement

TL;DR

This paper introduces a general analytic method to evaluate time-dependent pointer states in quantum systems, identifying conditions for their time independence, which is crucial for understanding measurement bases and decoherence processes.

Contribution

It generalizes existing theories by linking the mathematical conditions for pointer states to Hamiltonian symmetries, enabling prediction of measurement bases in various regimes.

Findings

Identifies conditions for time-independent pointer states including quantum decoherence limits.

Provides a method to predict preferred measurement bases based on system-environment Hamiltonian symmetries.

Analyzes regimes where pointer states are time-dependent, affecting decoherence times.

Abstract

We present a general analytic method for evaluating the generally time-dependent pointer states of a subsystem, which are defined by their capability not to entangle with the states of another subsystem. In this way, we show how in practice the global state of the system and the environment may evolve into a diagonal state as a result of the natural evolution of the total composite system. We explore the conditions under which the pointer states of the system become independent of time; so that a preferred basis of measurement can be realized. As we show, these conditions include the so-called quantum limit of decoherence and the so-called quantum measurement limit; as well as some other specific conditions which are discussed in the paper. We relate the mathematical conditions for having time-independent pointer states to some classes of possible symmetries in the Hamiltonian of the total composite system. Indeed, our theory would serve as a generalization of the existing theory for determination of the preferred basis of measurement. By exploiting this new theory we can obtain those regimes of the parameter space for a given total Hamiltonian defining our system-environment model for which a preferred basis of measurement can be realized. Moreover, we can predict the corresponding preferred basis of measurement for each regime. We can also obtain the time-dependent pointer states of the system and the environment in most of the other regimes where the pointer states of the system are time-dependent and a preferred basis of measurement cannot be realized at all. This ability to obtain time-dependent pointer states is specifically important in decoherence studies; as pointer states correspond to those initial conditions for the state of the system and the environment for which we can have longer decoherence times.