  Contrary to conventional quantum mechanics, which treats measurement as
instantaneous, here we explore a model for finite-time measurement. The main
two-level system interacts with the measurement apparatus in a Markovian way
described by the Lindblad equation, and with an environment, which does not
include the measuring apparatus. To analyse the environmental effects on the
final density operator, we use the Redfield approach, allowing us to consider a
non-Markovian noise. In the present hybrid theory, to trace out the
environmental degrees of freedom, we use a previously-developed analytic method
based on superoperator algebra and Nakajima-Zwanzig superoperators. Here, we
analyse two types of system-environment interaction, phase and amplitude
damping, which allows us to conclude that, in general, a finite-time quantum
measurement performed during a certain period is more efficient than an
instantaneous measurement performed at the end of it, because the rate of
change of the populations is attenuated by the system-measurement apparatus
interaction.
