Entanglement polygon inequality in qubit systems

Xiao-Feng Qian (1) , Miguel Alonso (1, 2, 3, 4, 5) , J Eberly (6)

1 University of Rochester [USA]
2 MOSAIC - MOSAIC
3 FRESNEL - Institut FRESNEL
4 ECM - École Centrale de Marseille
5 AMU - Aix Marseille Université
6 Department of Physics and Astronomy [Rochester]

We prove a set of tight entanglement inequalities for arbitrary N-qubit pure states. By focusing on all bi-partite marginal entanglements between each single qubit and its remaining partners, we show that the inequalities provide an upper bound for each marginal entanglement, while the known monogamy relation establishes the lower bound. The restrictions and sharing properties associated with the inequalities are further analyzed with a geometric polytope approach, and examples of three-qubit GHZ-class and W-class entangled states are presented to illustrate the results.

Mots clés: multiparty entanglement; entanglement restriction; entanglement sharing

Domaines: Physique [physics]; Physique Quantique [quant-ph]

Xiao-Feng Qian, Miguel Alonso, J Eberly. Entanglement polygon inequality in qubit systems. New Journal of Physics, 2018, 20 (6), ⟨10.1088/1367-2630/aac3be⟩. ⟨hal-01814150⟩