Locating overlap information in quantum systems

When discussing the black hole information problem the term ‘‘information flow’’ is frequently used in a rather loose fashion. In this paper I attempt to make this notion more concrete. I consider a Hilbert space which is constructed as a tensor product of two subspaces (representing, for example, inside and outside the black hole). I discuss how the system has the capacity to contain information which is in neither of the subspaces. I attempt to quantify the amount of information located in each of the two subspaces, and elsewere, and analyze the exent to which unitary evolution can correspond to ‘‘information flow.’’ I define the notion of ‘‘overlap information’’ which appears to be well suited to the problem.