How much time does a measurement take?

TL;DR

This paper derives an expression for the duration of quantum measurements using the Lindblad equation, showing it depends on system-measurer coupling and is unaffected by observable commutation, with strong coupling reducing measurement time.

Contribution

It provides an analytic formula for measurement time in quantum systems considering weak coupling and explores effects of strong coupling through numerical analysis.

Findings

Measurement time depends solely on system-measurer coupling.

Strong system-environment coupling decreases measurement duration.

The derived expression serves as an upper limit for measurement time.

Abstract

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.