A Genuine Multipartite Entanglement Measure Generated by the Parametrized Entanglement Measure

Abstract

A genuine multipartite entanglement measure based on the geometric method is investigated in this paper. This measure has desirable properties for quantifying the genuine multipartite entanglement. A lower bound of the genuine multipartite entanglement measure derived with the fidelity‐based method is then presented. The advantages of the measure proposed here with other measures are also presented. At last, examples are presented to show that the genuine entanglement measure has distinct entanglement ordering from other measures.

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“…Based on the results in Ref. [46], we can attain q-2-GM concurrence of W state is strictly less than that of GHZ state in multiqubit systems.…”

“…It is obvious that the q-k-GM concurrence can be thought of as a generalization of q-concurrence [39] or Tsallis-q entanglement with a specific q [45], which is considered from different perspective than q-k-ME concurrence [22]. Besides, q-k-GM concurrence can also be treated as the generalized form of genuine multipartite entanglement measure, GBC [35] and geometric mean of q-concurrence G q (GqC) [46].…”

“…The q-2-GM concurrence and GqC [46] are two different kinds of entanglement measures for arbitrary quantum states, but in terms of pure states, one can obtain the relation G q−2 (|ψ⟩) = 2G q (|ψ⟩). Based on the results in Ref.…”

“…Here ρ A and δ A are respectively the reduced density matrixes of |ϕ⟩ AB and |φ⟩ AB , the first inequality holds because C q (|ϕ⟩ AB ) = 1−Tr(ρ q A ) satisfies subadditivity [37], the second inequality can be obtained according to the relation (a+b…”

“…Although there are a battery of entanglement measures to describe the entanglement distribution of multipartite quantum states [34][35][36][37][38], the difficulty of calculating how much entanglement a mixed state contains remains. However, MoE, in fact, offers an upper bound for bipartite sharability of entanglement in multipartite sys-tems, whereas its dual (polygamy of entanglement) gives a lower bound for distribution of bipartite entanglement.…”