Residual entanglement and sudden death: A direct connection

TL;DR

This paper investigates the relationship between residual entanglement and entanglement sudden death in tripartite and four-partite quantum systems, revealing that residual entanglement appears in tripartite systems during sudden death, but not necessarily in four-partite systems.

Contribution

It establishes a direct connection between entanglement sudden death and residual entanglement in tripartite systems, and clarifies their relationship in four-partite systems.

Findings

Residual entanglement appears during entanglement sudden death in tripartite systems.

In four-partite systems, residual entanglement is not necessarily linked to sudden death.

If sudden death occurs in some partition, residual entanglement will be present.

Abstract

We explore the results of [V. Coffman, et al., Phys. Rev. A 61 (2000) 052306] derived for general tripartite states in a dynamical context. We study a class of physically motivated tripartite systems. We show that whenever entanglement sudden death occurs in one of the partitions residual entanglement will appear. For fourpartite systems however, the appearance of residual entanglement is not conditioned by sudden death of entanglement. We can only say that if sudden death of entanglement occurs in some partition there will certainly be residual entanglement.