>But (afaik) measuring means disturbing, because you have to exchange some energy with the system in order to perform the measurement.
This isn't necessarily true; QM allows what's called interaction-free measurement. Say you have a particle that's in a superposition of two states (or places, or whatever), which I'll call A and B. You do something that'll interact (and detect) it if it's in A. If you didn't detect it, that means you've effectively measured it as being in B.
You can also turn it around, and use a particle in a superposition to see if an object (that it would interact with if it's in state A) exists; if the object exists, the possibility of interacting with it will destroy interference effects between the parts of the particle's superposition, allowing you to infer the existence of the object. The Elitzur–Vaidman bomb tester (https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester) is an extreme example of this: it lets you verify that a bomb is "live" (will explode if interacted with), with only a 50% chance of setting it off.
Another example is the interaction-free version of the quantum Zeno effect. The quantum Zeno effect is that (under the right circumstances) a particle can be trapped in a particular state by continuously measuring whether it's still in the state. In the interaction-free version, you use something that'll interact if the particle ever leaves the state... and it never does. This has actually been done; see https://www.nature.com/articles/ncomms7811?WT.ec_id=NCOMMS-2...
This isn't necessarily true; QM allows what's called interaction-free measurement. Say you have a particle that's in a superposition of two states (or places, or whatever), which I'll call A and B. You do something that'll interact (and detect) it if it's in A. If you didn't detect it, that means you've effectively measured it as being in B.
You can also turn it around, and use a particle in a superposition to see if an object (that it would interact with if it's in state A) exists; if the object exists, the possibility of interacting with it will destroy interference effects between the parts of the particle's superposition, allowing you to infer the existence of the object. The Elitzur–Vaidman bomb tester (https://en.wikipedia.org/wiki/Elitzur–Vaidman_bomb_tester) is an extreme example of this: it lets you verify that a bomb is "live" (will explode if interacted with), with only a 50% chance of setting it off.
Another example is the interaction-free version of the quantum Zeno effect. The quantum Zeno effect is that (under the right circumstances) a particle can be trapped in a particular state by continuously measuring whether it's still in the state. In the interaction-free version, you use something that'll interact if the particle ever leaves the state... and it never does. This has actually been done; see https://www.nature.com/articles/ncomms7811?WT.ec_id=NCOMMS-2...