Structure of Quantum Theory

In Nat Commun 10, 1361 (2019) we showed that the measurement postulates of quantum theory were operationally redundant, namely any theory with modified measurement postulates was not a well-defined operational theory. Theories which share the same pure states, unitary dynamics and pure state composition rule as quantum theory but differ in the allowed measurements violate core operationally consistency properties such as no-signalling and associativity of composition. However, one additional assumption was needed to prove the main theorem of Nat Commun 10, 1361 (2019): "For a finite dimensional quantum system, it is possible to perform state tomography using a finite number of measurements".

In this talk I will show that this assumption can be removed, thus deriving the measurement postulates of quantum theory purely within the operational framework, without any further auxiliary assumptions. I discuss a consistent infinite dimensional alternative measurement postulate for single and bi-partite systems and then argue that associativity of discarding of systems rules out any modified measurement postulates for three or more systems. I show that our strengthened measurement theorem now formally rules out Scott Aaronson's proposed p-norm modified Born rule.

In a final part, I give an overview of some critical comments made by Adrian Kent and Blake Stacey as well as discuss some broader implications of this work.