Distribution of entanglement in multipartite systems
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Distribution of entanglement for the multipartite systems is characterized through monogamy and polygamy relations. In this paper, we study the xth power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations based on the nonnegative power of Tsallis-q entanglement are obtained for N-qubit states and are shown to be tighter than existing relation. We find that for any tripartite mixed state, the Tsallis-q entanglement follows a polygamy relation. This polygamy relation also holds for the multi-qubit systems. The polygamy relations of the Tsallis-q entanglement, that are uniquely defined for generalized multi-qubit W-class states, and partially coherent superposition states are also examined. Moreover, the tighter monogamy bounds for concurrence of assistance and negativity of assistance are also established for these states, which gives more accurate bounds than existing relations.
KeywordsConcurrence Monogamy relations Polygamy relations Negativity Tsallis-q entanglement W-class state PCS states
This work was supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (No. 2016R1A2B2014462), by the Basic Science Research Program through the NRF funded by the Ministry of Education (No. 2018R1D1A1B07050584), and ICT R&D program of MSIP/IITP [R0190-15-2030, Reliable crypto-system standards and core technology development for secure quantum key distribution network].