Maximizing genuine multipartite entanglement of N mixed qubits

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.

6 pages, 4 figures

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Cited by in corpus (7)

• Entanglement universality of two-qubit X-states
• Random Sampling of Quantum States: A Survey of Methods
• A Variational Approach to the Quantum Separability Problem
• Tri-partite non-maximally entangled mixed states as a resource for optimum controlled quantum teleportation fidelity
• Fortran code for generating random probability vectors, unitaries, and quantum states
• Bounding the entanglement of N qubits with only four measurements
• Maximally genuine multipartite entangled mixed X-states of N-qubits