  Encoding information in quantum systems can offer surprising advantages but
at the same time there are limitations that arise from the fact that measuring
an observable may disturb the state of the quantum system. In our work, we
provide an in-depth analysis of a simple question: What happens when we perform
two measurements sequentially on the same quantum system? This question touches
upon some fundamental properties of quantum mechanics, namely the uncertainty
principle and the complementarity of quantum measurements. Our results have
interesting consequences, for example they can provide a simple proof of the
optimal quantum strategy in the famous Clauser-Horne-Shimony-Holt game.
Moreover, we show that the way information is encoded in quantum systems can
provide a different perspective in understanding other fundamental aspects of
quantum information, like non-locality and quantum cryptography. We prove some
strong equivalences between these notions and provide a number of applications
in all areas.
