A decision-theoretic approach to dealing with uncertainty in quantum mechanics
This work addresses foundational issues in quantum mechanics for physicists and philosophers, offering a novel theoretical approach but is incremental relative to existing decision-theoretic models.
The authors tackled the problem of uncertainty in quantum mechanics by developing a decision-theoretic framework that separates probability theory from quantum mechanics, allowing for imprecise probabilities and encapsulating Born's rule in utility functions.
We provide a decision-theoretic framework for dealing with uncertainty in quantum mechanics. This uncertainty is two-fold: on the one hand there may be uncertainty about the state the quantum system is in, and on the other hand, as is essential to quantum mechanical uncertainty, even if the quantum state is known, measurements may still produce an uncertain outcome. In our framework, measurements therefore play the role of acts with an uncertain outcome and our simple decision-theoretic postulates ensure that Born's rule is encapsulated in the utility functions associated with such acts. This approach allows us to uncouple (precise) probability theory from quantum mechanics, in the sense that it leaves room for a more general, so-called imprecise probabilities approach. We discuss the mathematical implications of our findings, which allow us to give a decision-theoretic foundation to recent seminal work by Benavoli, Facchini and Zaffalon, and we compare our approach to earlier and different approaches by Deutsch and Wallace.