Non-Hermitian quantum mechanics and open quantum systems

Although quantum physics is Hermitian, non-Hermitian approches often turn out to be quite useful, e.g., in order to impose absorbing boundary conditions to unbound systems. Typically, non-Hermicity induces a loss in the norm of the wave function - corresponding to particles being removed from the system. Since such a removal also removes the memory of the particles, it is Markovian, the Schrödinger equation is not fully able to describe such processes. Within the formalism of open quantum system, however, it may be done.
 
Although the evolution of an open quantum system is not unitary, we may still keep information about lost particles in the sense that we keep a record of what we remove. Actually, this is quite similar to what goes on in a detector - also when it comes to loss of coherence. I will try and elaborate on this analogy and argue that in simulations, absorbers may abs act as a detector under certain conditions.