Epistemic restrictions in Hilbert space quantum mechanics

A resolution of the quantum measurement problem(s) using the consistent histories interpretation yields in a rather natural way a restriction on what an observer can know about a quantum system, one that is also consistent with some results in quantum information theory. This analysis provides a quantum mechanical understanding of some recent work that shows that certain kinds of quantum behavior are exhibited by a fully classical model if by hypothesis an observer's knowledge of its state is appropriately limited.

Figure 1

(a) Phase space $\Gamma$. Properties are indicated by collections of points such as $\mathcal{P}$ and $\mathcal{Q}$. (b) Hilbert space with properties represented by rays such as $\mathcal{P}$, ${\mathcal{P}}^{\perp }$, and $\mathcal{Q}$.