Unified Monogamy Relations of Multipartite Entanglement

Abstract

Unified-(q, s) entanglement is a generalized bipartite entanglement measure, which encompasses Tsallis-q entanglement, Rényi-q entanglement, and entanglement of formation as its special cases. We first provide the extended (q; s) region of the generalized analytic formula of . Then, the monogamy relation based on the squared for arbitrary multiqubit mixed states is proved. The monogamy relation proved in this paper enables us to construct an entanglement indicator that can be utilized to identify all genuine multiqubit entangled states even the cases where three tangle of concurrence loses its efficiency. It is shown that this monogamy relation also holds true for the generalized W-class state. The αth power based general monogamy and polygamy inequalities are established for tripartite qubit states.

Unified monogamy relation of entanglement measures

“…Our main goal in this paper is to present unified and tightened monogamy relations of entanglement measures encompassing the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, and Rényiq entropy, and Unified (q, s) entropy for entangled qubit systems. The new monogamy inequalities with larger lower bounds also contain recent results [25,28] as special cases. Moreover, we explore the generic feature of high-dimensional entangles systems going beyond qubit systems.…”

“…The so-called CKW inequality was later extended to arbitrary N -qubit systems [18]. Interestingly, it was further proven that similar multiqubit monogamy inequalities can be established for the squared negativity, the squared convex-roof extended negativity [19], the square of EOF [20][21][22], Tsallis-q entropy [11], the squared Tsallis-q entropy [23], Rényi-q entropy [14], the squared Rényi-q entropy [24], Unified-(q, s) entropy [15], and the squared unified-(q, s) entropy [25].…”

“…Generally, for an entanglement measure E one can get a quantity E αc satisfying the monogamy inequality (21) for entangled qubit systems even if E is not monogamous. Different values of α c exist for aforementioned entanglement measures [18][19][20][21][22][23][24][25]. Similar result cannot be proved for high-dimensional systems.…”

“…where the infimum is taken over all possible pure state decompositions of ρ AB = i p i |φ i AB φ i | with i p i = 1, and p i ≥ 0. It's worth pointing out that there exists a functional relation [25] U q,s (|φ…”

“…Other results are to tighten the monogamy inequalities which are useful for featuring multipartite entangled systems in entanglement distributions [28][29][30][31]. So far, although lots of monogamy relations are proposed [18][19][20][21][22][23][24][25][26][27][28][29][30][31], there is a few unified monogamy relation for the aforementioned entanglement measures of bipartite systems [25]. Our main goal in this paper is to present unified and tightened monogamy relations of entanglement measures encompassing the concurrence, the negativity, the entanglement of formation, Tsallis-q entropy, and Rényiq entropy, and Unified (q, s) entropy for entangled qubit systems.…”