In short, the principle to be assumed is that if a measurement yields no information, then the system being measured has not been disturbed.
If you learn nothing from measuring a system, then you can’t have disturbed it.
Consider the famous Schrodinger’s cat paradox, a thought experiment in which a cat in a box simultaneously exists in two states (this is known as a ‘quantum superposition’). According to quantum theory it is possible that the cat is both dead and alive – until, that is, the cat’s state of health is ‘measured’ by opening the box. When the box is opened, allowing the health of the cat to be measured, the superposition collapses and the cat ends up definitively dead or alive. The measurement has disturbed the cat.
Corsin was trying to find a general way to describe the effects of measurements on states, a problem that he found impossible to solve. In an attempt to make progress, he wrote down features that a ‘sensible’ answer should have. This property of information gain versus disturbance was on the list. He then noticed that if he imposed the property as a principle, some theories would fail.
Corsin and Stephanie are keen to point out it’s still not the whole answer to the big ‘why’ question: theories other than quantum physics, including classical physics, are compatible with the principle. But as researchers compile lists of principles that each rule out some theories to reach a set that singles out quantum physics, the principle of information gain versus disturbance seems like a good one to include