# Purification of quantum trajectories

**Authors:** Hans Maassen, Burkhard Kümmerer  
**arXiv:** [quant-ph/0505084](https://arxiv.org/abs/quant-ph/0505084)  
**Date:** 2005-05-11  
**Summary page:** https://www.summarizepaper.com/en/paper/quant-ph--0505084v1/

## Abstract

We prove that the quantum trajectory of repeated perfect measurement on a finite quantum system either asymptotically purifies, or hits upon a family of `dark' subspaces, where the time evolution is unitary.