Locating Overlap Information in Quantum Systems

TL;DR

This paper introduces a framework for quantifying and analyzing how information is distributed and flows within quantum systems, especially in the context of black hole information paradox, using the concept of overlap information.

Contribution

It proposes a new method to quantify overlap information in quantum systems, providing a concrete approach to understanding information localization and flow.

Findings

Defined the concept of overlap information for quantum systems.

Provided a quantitative measure for information distribution across subspaces.

Analyzed how unitary evolution affects information flow.

Abstract

When discussing the black hole information problem the term ``information flow'' is frequently used in a rather loose fashion. In this article 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 elsewhere, and analyze the extent 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.