Multi-partite analysis of average-subsystem entropies

TL;DR

This paper extends the analysis of average subsystem entropies from bipartite to multi-partite quantum systems, providing new calculations and bounds, and exploring the role of environments in small subsystems.

Contribution

It introduces new methods for analyzing average subsystem entropies in multi-partite systems, including calculations of average tangle and bounds on average concurrence.

Findings

Extended analysis to tripartite and multi-partite systems

Derived bounds on average concurrence

Introduced the concept of environment coupling in small subsystems

Abstract

So-called average subsystem entropies are defined by first taking partial traces over some pure state to define density matrices, then calculating the subsystem entropies, and finally averaging over the pure states to define the average subsystem entropies. These quantities are standard tools in quantum information theory, most typically applied in bipartite systems. We shall first present some extensions to the usual bipartite analysis, (including a calculation of the average tangle, and a bound on the average concurrence), follow this with some useful results for tripartite systems, and finally extend the discussion to arbitrary multi-partite systems. A particularly nice feature of tri-partite and multi-partite analyses is that this framework allows one to introduce an "environment" for small subsystems to couple to.