Multipartite entanglement measure for all discrete systems

TL;DR

This paper introduces a new operational entanglement measure for all discrete quantum systems, enabling classification and analysis of multipartite entanglement with practical bounds and interpretability.

Contribution

It presents a novel entanglement measure based on a multidimensional complementarity relation, applicable to any discrete quantum system, including mixed states.

Findings

The measure separates different classes of entanglement using flip operators.

Bounds on the m-flip concurrence are derived for mixed states.

Application to three-qubit systems reveals physical differences in entanglement types.

Abstract

Via a multidimensional complementarity relation we derive a novel operational entanglement measure for any discrete quantum system, i.e. for any multidimensional and multipartite system. This new measure admits a separation into different classes of entanglement obtained by using a flip operator 2,3,...,n times, defining a m-flip concurrence. For mixed states bounds on this m-flip concurrence can be obtained. Moreover, the information content of a n partite multidimensional system admits an intuitive interpretation. Explicitly, the three qubits system is analyzed and the physical difference in entanglement of the W-state, the GHZ state or the bi-separable state is revealed.