Superactivation and Incompressibility of Genuine Multipartite Entanglement

TL;DR

This paper investigates the phenomenon of superactivation in genuine multipartite entanglement, providing systematic methods, criteria, and a proof of the existence of incompressible entanglement states that resist reduction to single-copy levels.

Contribution

It introduces a comprehensive framework for understanding superactivation of multipartite entanglement, including new criteria and the concept of incompressible entanglement states.

Findings

Development of systematic methods based on symmetries for studying superactivation.

Introduction of criteria and quantitative measures for superactivation.

Proof of existence of states with incompressible entanglement that cannot be simplified to single copies.

Abstract

Quantum correlations in the form of entanglement, quantum steering or Bell nonlocality are resources for various information-processing tasks, but their detailed quantification and characterization remain complicated. One counter-intuitive effect is the phenomenon of superactivation, meaning that two copies of a quantum state may exhibit forms of correlations which are absent on the single-copy level. We develop a systematic approach towards a full understanding of this phenomenon using the paradigm of genuine multipartite entanglement. We introduce systematic methods for studying superactivation of entanglement based on symmetries and generalized notions of multipartite distillability. With this, we present novel criteria for superactivation as well as a quantitative theory of it. Finally, we prove the existence of incompressible entanglement, meaning that there are quantum states for which superactivated multipartite entanglement cannot be reduced to the single-copy level.