Lindbladian-Induced Alignment in Quantum Measurements

TL;DR

This paper introduces a Lindbladian framework for continuous quantum measurement that ensures a clear transition from superposition to definite outcomes, incorporating environment adaptability and finite transition times.

Contribution

It formalizes a Lindbladian approach to quantum measurement that accounts for environment adaptation and finite transition durations, differing from previous models.

Findings

Transition duration estimated for a simple spin model

Lindbladian form ensures unambiguous measurement outcomes

Environment adapts to measurement mode

Abstract

An expression of the Lindbladian form is proposed that ensures an unambiguous time-continuous reduction of the initial system-pointer wave-packet to one in which the readings and the observable's values are aligned, formalized as the transition from an outer product to an inner product of the system's and apparatus' density matrices. The jump operators are in the basis of the observables, with uniquely determined parameters derived from the measurement set-up (thereby differing from S. Weinberg's Lindbladian resolution of wave-packet formalism) and conforming to Born's probability rules. The novelty lies in formalising the adaptability of the surroundings (including the measuring device) to the mode of observation. Accordingly, the transition is of finite duration (in contrast to its instantaneousness in the von Neumann's formulation). This duration is estimated for a simple half-spin-like model.