Complementary quantum correlations among multipartite systems

Abstract

We study the monogamy and polygamy relations related to quantum correlations for multipartite quantum systems. General monogamy relations are presented for the αth (0 ≤ α ≤ γ, γ ≥ 2) power of quantum correlation, and general polygamy relations are given for the βth (β ≥ δ, 0 ≤ δ ≤ 1) power of quantum correlation. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of α and β. Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given.

Monogamy and polygamy relations of quantum correlations for multipartite systems

“…2 and r ≥ 2. Using concurrence as the quantum correlation measure, our Theorem 1 is a generalization of Theorem 1 in [15]. Remark 2.…”

“…Tighter polygamy inequalities for the βth (0 ≤ β ≤ 1) power of concurrence [12] and the CREN [13] were investigated. Although lots of monogamy and polygamy relations were proposed, there were only a few monogamy relations for the αth (0 ≤ α ≤ 1) power of entanglement measures and polygamy relations of the βth power for β ≥ 1 [14,15]. Besides concurrence and negativity, unified-(q, s) entanglement also have monogamy and polygamy relations.…”

“…Besides concurrence and negativity, unified-(q, s) entanglement also have monogamy and polygamy relations. Using unified-(q, s) entanglement with real parameters q and s, a class of monogamy and polygamy inequalities of multi-qubit systems were proposed [14][15][16][17][18][19][20].…”

Multipartite uncertainty relation with quantum memory

“…This generalized entropic uncertainty depends on the conditional von-Neumann entropies, Holevo quantities, and the mutual information. We expect that the inequality will bring on more potential applications in quantum information and communication, e.g., entanglement detection 64 , multipartite entanglement-structure detection 65 , witnessing multipartite entanglement 66 , detection of genuine multipartite entanglement in multipartite systems 67 , exploring the efficient multipartite entanglement criteria 68 – 70 , analyzing the monogamy and polygamy relations of multipartite quantum states 71 , 72 , and so on. It means that our multipartite uncertainty relation will have significant applications in entanglement detection and precision measurements.…”

Monogamy and trade-off relations for correlated quantum coherence

“…This indicates that there is a limitation in the distribution of entanglement [16]. This unique property, known as entanglement monogamy, has received a lot of attention by researchers [17][18][19][20][21]. Mathematically, for a tripartite quantum system described by the density matrix ρ A,B,C , the monogamy relation for an arbitrary quantum correlation measure Q is expressed by…”