Tighter entanglement monogamy relations of qubit systems

Abstract

Monogamy relations characterize the distributions of entanglement in multipartite systems. We investigate monogamy relations related to the concurrence C and the entanglement of formation E. We present new entanglement monogamy relations satisfied by the α-th power of concurrence for all α ≥ 2, and the α-th power of the entanglement of formation for all α ≥ √ 2. These monogamy relations are shown to be tighter than the existing ones.

Tighter Constraints of Multiqubit Entanglement*

“…see that our result is better than the result (5) in [22] for β ≥ 2, hence better than (3) and (4) given in [21,23], see We now discuss the polygamy relations for the CoA of C a (|ψ A|B1···BN−1 ) for 0 ≤ β ≤ 2. We have the following Theorem.…”

“…for β ≥ √ 2 and t = β As (1+k) t −1 k t ≥ 2 t − 1 for t ≥ 1 and 0 < k ≤ 1, our new monogamy relations (26) and (30) are tighter than the ones given in [21][22][23]. Also, for 0 < k ≤ 1 and β ≥ 2, the smaller k is, the tighter inequalities (26) and (30) are.…”

“…[21,22], the authors proved that the squared concurrence and CREN satisfy the monogamy inequalities in multiqubit systems for β ≥ 2. It has also been shown that the EoF satisfies monogamy relations when β ≥ √ 2 [21][22][23]. Besides, the Tsallis-q entanglement and Rényi-α entanglement satisfy monogamy relations when β ≥ 1 [14,[22][23][24] for some cases.…”

“…It has also been shown that the EoF satisfies monogamy relations when β ≥ √ 2 [21][22][23]. Besides, the Tsallis-q entanglement and Rényi-α entanglement satisfy monogamy relations when β ≥ 1 [14,[22][23][24] for some cases. Moreover, the corresponding polygamy relations have also been established [16-18, 20, 25, 26].…”

Strong polygamy and monogamy relations for multipartite quantum systems

“…The first monogamy relation was proven for arbitrary three-qubit states based on the squared concurrence. Later, various monogamy inequalities have been established for a number of entanglement measures in multipartite quantum systems [1][2][3][4][5][6][7][8]. Polygamy relations are also generalized to multiqubit systems [9] and arbitrary dimensional multipartite states [3][4][5].…”