Structure of Quantum Theory

For QBism, measurement is the fundamental thing. On the face of it, however, dynamics is odd. Like the other objects of the theory, it is a personal judgment, but why should an agent feel compelled to update her quantum states in the precise way the quantum formalism seems to mandate? Why are there any constraints at all on how an agent’s state assignments should change over time when nothing is happening for her by way of an action on a system or a consequence arising from it? To answer this, I will first show that the standard measurement-update rule needs no dynamical grounding, contrary to how it is often portrayed. Then, I will show that dynamics -- the CPTP maps of ordinary quantum mechanics -- follows from a representation theorem needing only diachronic coherence and a single judgment of indifference. Specifically, an agent who judges some hypothetical intervening measurement irrelevant to her present gambles about a farther future is compelled to adopt a definite state-update rule across that period of inaction.

This talk is based on https://arxiv.org/abs/2312.14112