An open quantum system can be described by the Lindblad master equation. If one wants to describe an open system, which is continously measured, one can describe such a system using a stochastic master equation. Without the measurement, the system state generally becomes more and more mixed, due to the dissipation caused by the environment. Therefore the purity $tr[\rho^2]$ generally becomes smaller. In contrast to that, I know that the purity of a continously measured 2-level system becomes 1 in the long time limit. The reason for that is, that the system state is collapsed into a pure state every time a measuremet is performed. I have two question regarding this:
- Do I have the right idea, when I picture this process as dissipation and continous measurement working against each other, trying to make the state more mixed/pure and in the long time limit, the measurement process "wins"?
- Does the result $tr[\rho^2] = 1$ in the long time limit also hold for infinite dimensional systems, like e.g. a continously measured open harmonic oscillator?
