Statistics of continuous weak linear measurement

One of the pillars of the scientific method is the fact that all scientific predictions and explanations of phenomena in the universe are testable. Testing in the context of physics involves the action of measuring. Thus, the measurement process plays an important role in physics.
While classically we all understand the idea of measurement in a very straightforward fashion, in quantum mechanics the concept of measurement departs fromour everyday experience in physics. In fact, although the quantum measurement obeys rather simple rules, its interpretation has been a subject of discussion since the beginning of the 20th century.
Some of the physics involved in the process of a quantum measurement have no classical analogues, challenging in this way our intuition: the famous paradox of a cat in a box is a clear example of this.