Maximizing genuine multipartite entanglement of N mixed qubits

TL;DR

This paper derives analytic expressions for the maximum genuine multipartite entanglement in N-qubit X-states given their mixedness, revealing how entanglement persists at higher mixedness levels as N increases.

Contribution

It introduces the class of maximally entangled N-qubit X-states for a given mixedness and identifies the critical mixedness threshold for entanglement.

Findings

Maximum entanglement states are characterized for N-qubit X-states.

Critical mixedness threshold for entanglement is derived.

Higher N allows entanglement at greater mixedness levels.

Abstract

Beyond the simplest case of bipartite qubits, the composite Hilbert space of multipartite systems is largely unexplored. In order to explore such systems, it is important to derive analytic expressions for parameters which characterize the system's state space. Two such parameters are the degree of genuine multipartite entanglement and the degree of mixedness of the system's state. We explore these two parameters for an N-qubit system whose density matrix has an X form. We derive the class of states that has the maximum amount of genuine multipartite entanglement for a given amount of mixedness. We compare our results with the existing results for the N=2 case. The critical amount of mixedness above which no N-qubit X-state possesses genuine multipartite entanglement is derived. It is found that as N increases, states with higher mixedness can still be entangled.