# Guaranteed emergence of genuine entanglement in 3-qubit evolving systems

## TL;DR

This paper analyzes conditions under which a two-qubit system interacting with a third qubit can evolve into genuinely entangled 3-qubit states, providing a classification of processes that guarantee entanglement emergence.

## Contribution

It establishes necessary and sufficient conditions on Kraus operators for generating various classes of 3-qubit entanglement from an initial two-qubit state.

## Key findings

- Classifies Kraus operators based on their ability to produce 3-qubit entanglement.
- Provides criteria to determine if evolved states are biseparable, W-, or GHZ-entangled.
- Lays groundwork for extending entanglement control to larger quantum systems.

## Abstract

Multipartite entanglement has been shown to be of particular relevance for a better understanding and exploitation of the dynamics and flow of entanglement in multiparty systems. This calls for analysis aimed at identifying the appropriate processes that guarantee the emergence of multipartite entanglement in a wide range of scenarios. Here we carry on such analysis considering a system of two initially entangled qubits, one of which is let to interact with a third qubit according to an arbitrary unitary evolution. We establish necessary and sufficient conditions on the corresponding Kraus operators, to discern whether the evolved state pertains to either one of the classes of 3-qubit pure states that exhibit some kind of entanglement, namely biseparable, W-, and GHZ- genuine entangled classes. Our results provide a classification of the Kraus operators according to their capacity of producing 3-qubit entanglement, and pave the way for extending the analysis to larger systems and determining the particular interactions that must be implemented in order to create, enhance and distribute entanglement in a specific manner.