Reasoning about quantum knowledge

Abstract

We construct a formal framework for investigating epistemic and temporal notions in the context of distributed quantum computation. While we rely on structures developed earlier, we stress that our notion of quantum knowledge makes sense more generally in any agent-based model for distributed quantum systems. Several arguments are given to support our view that an agent's possibility relation should not be based on the reduced density matrix, but rather on local classical states and local quantum operations. In this way, we are able to analyse distributed primitives such as superdense coding and teleportation, obtaining interesting conclusions as to how the knowledge of individual agents evolves. We show explicitly that the knowledge transfer in teleportation is essentially classical, in that eventually, the receiving agent knows that its state is equal to the initial state of the sender. The relevant epistemic statements for teleportation deal with this correlation rather than with the actual quantum state, which is unknown throughout the protocol.