Tighter Weighted Polygamy Inequalities of Multipartite Entanglement in Arbitrary-Dimensional Quantum Systems

Abstract

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in [Phys. Rev. A 97, 042332 (2018)].

Tighter monogamy and polygamy relations of multiparty quantum entanglement

“…In this paper, we establish new classes of tight monogamy and polygamy relations of multiparty entanglement for arbitrary quantum states, based on the power of the bipartite measure of entanglement and the entanglement of assistance. We show that these new monogamy and polygamy relations are tighter than the results in [20][21][22][23][24][25][26][27].…”

“…Remark 2. It is easy to see that Theorem 4 is generally tighter than the polygamy relations in terms of the Hamming weight [22][23][24][25]27].…”

“…Example 1 : For the four-qubit W state [27] the result in [25,26] with k = 2. The ( yellow ) line f represents the upper bound from the result in [27].…”

“…2 . Thus Theorems 1 and 4 are better than the monogamy and polygamy relations in terms of the Hamming weight [22][23][24][25]27].…”

“…Later, it was shown that the same polygamy inequality was also generalized in terms of various assisted entanglements [17][18][19]. Recently, a class of tight monogamy relations and polygamy relations were derived in multiparty quantum systems [20][21][22][23][24][25][26][27][28]. In this paper, we establish new classes of tight monogamy and polygamy relations of multiparty entanglement for arbitrary quantum states, based on the power of the bipartite measure of entanglement and the entanglement of assistance.…”