Quantum and Classical Bayesian Agents

The paradigm of multiple interacting agents who each utilize quantum mechanics is central to much of the recent activity in quantum foundations and quantum information. Relevant work in the latter broadly seeks to identify what advantages quantum theory affords us in the multi-agent setting, but, as recent foundational work highlights, there remains confusion over how to appropriately work in such a setting so as to avoid inconsistencies. A careful and consistent treatment of multiple users of quantum theory would allow us to properly interpret extant work and may suggest new approaches in other areas such as algorithm design. The natural starting point for an agent-based treatment is given by the Quantum Bayesian (QBist) approach. Adopting this, we outline a general approach to modeling rational decision making agents who adopt a normative constraint on expectations for the consequences of hypothetical actions. Agents who universally adopt quantum or classical mechanics in all of their reasoning are seen to be special cases of this approach. As an illustration, we consider quantum and classical agents in two physical scenarios: agents receiving data from an exogenous, non-agential, source and two or more agents interacting with each other.