Entanglement Sudden Death in Three Qubit X-States

TL;DR

This paper investigates the entanglement dynamics of three-qubit X-states under decoherence, revealing phenomena like entanglement sudden death and non-standard entanglement behavior, with extensions to multi-qubit states and bounds on concurrence.

Contribution

It introduces a detailed analysis of entanglement sudden death in three-qubit X-states, extending negativity measures to arbitrary qubit numbers and providing bounds on concurrence.

Findings

Entanglement sudden death observed in three-qubit X-states.

Non-standard behavior of tripartite negativity, including sudden appearance.

Derived lower bounds on three-qubit X-state concurrence.

Abstract

I explore the entanglement dynamics of a three qubit system in an initial X-state undergoing decoherence including the possible exhibition of entanglement sudden death (ESD). To quantify entanglement I utilize negativity measures and make use of appropriate entanglement witnesses. The negativity results are then extended to X-states with an arbitraty number of qubits. I also demonstrate non-standard behavior of the tri-partite negativity entanglement metric, its sudden appearance after some amount of decoherence followed quickly by its disappearance. Finally, I solve for a lower bound on the three qubit X-state concurrence, demonstrate when this bound goes to zero, and outline simplifcations for the calculation of higher order X-state concurrences.