Geometric mean of bipartite concurrences as a genuine multipartite entanglement measure

Abstract

In this work we propose the geometric mean of bipartite concurrences as a genuine multipartite entanglement measure. This measure achieves the maximum value for absolutely maximally entangled states and has desirable properties for quantifying potential quantum resources. The simplicity and symmetry in the definition facilitates its computation for various multipartite entangled states including the GHZ states and the $W$ states. With explicit examples we show that our measure results in distinct entanglement orderings from other measures, and can detect differences in certain types of genuine multipartite entanglement while other measures cannot. These results justify the practical application of our measure for tasks involving genuine multipartite entanglement.

8 pages, 4 figures; Comments are welcome!

References in corpus (12)

• Entanglement detection
• Multi-party entanglement in graph states
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Entanglement Certification $-$ From Theory to Experiment
• Taming multiparticle entanglement
• Concurrence of arbitrary dimensional bipartite quantum states
• Measure of genuine multipartite entanglement with computable lower bounds
• Multipartite entanglement in spin chains
• Genuinely Multipartite Concurrence of N-qubit X-matrices
• Hierarchies of Geometric Entanglement
• Two computable sets of multipartite entanglement measures
• Evaluable multipartite entanglement measures: are multipartite concurrences entanglement monotones?