Abstract
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.
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Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865 (2009)
Qaisar, S., Rehman, J.U., Jeong, Y., Shin, H.: Practical deterministic secure quantum communication in a lossy channel. Prog Theor Exp Phys 2017(4), 041A01 (2017)
Kumar, A., Roy, S.S., Pal, A.K., Prabhu, R., De, A.S., Sen, U.: Conclusive identification of quantum channels via monogamy of quantum correlations. Phys. Rev. A 380(43), 3588–3594 (2016)
Coffman, V., Kundu, J., Wootters, W.K.: Distributed entanglement. Phys. Rev. A 61(5), 052306 (2000)
Osborne, T.J., Verstraete, F.: General monogamy inequality for bipartite qubit entanglement. Phys. Rev. Lett. 96(22), 220503 (2006)
de Oliveira, T.R., Cornelio, M.F., Fanchini, F.F.: Monogamy of entanglement of formation. Phys. Rev. A 89(3), 034303 (2014)
Ou, Y.C., Fan, H.: Monogamy inequality in terms of negativity for three-qubit states. Phys. Rev. A 75(6), 062308 (2007)
Kim, J.S., Das, A., Sanders, B.C.: Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity. Phys. Rev. A 79(1), 012329 (2009)
Kim, J.S.: Tsallis entropy and entanglement constraints in multiqubit systems. Phys. Rev. A 81(6), 062328 (2010)
Luo, Y., Tian, T., Shao, L.H., Li, Y.: General monogamy of Tsallis \(q\)-entropy entanglement in multiqubit systems. Phys. Rev. A 93(6), 062340 (2016)
Kim, J.S., Sanders, B.C.: Monogamy of multi-qubit entanglement using Rényi entropy. J. Phys. A: Math. Theor. 43(44), 445305 (2010)
Kim, J.S., Sanders, B.C.: Unified entropy, entanglement measures and monogamy of multi-party entanglement. J. Phys. A: Math. Theor. 44(29), 295303 (2011)
Gour, G., Bandyopadhyay, S., Sanders, B.C.: Dual monogamy inequality for entanglement. J. Math. Phys. 48(1), 012108 (2007)
Buscemi, F., Gour, G., Kim, J.S.: Polygamy of distributed entanglement. Phys. Rev. A 80, 012324 (2009)
Kim, J.S., Sanders, B.C.: Generalized W-class state and its monogamy relation. J. Phys. A: Math. Theor. 41(49), 495301 (2008)
Kim, J.S.: Strong monogamy of quantum entanglement for multiqubit W-class states. Phys. Rev. A 90(6), 062306 (2014)
Kim, J.S.: Strong monogamy of multiparty quantum entanglement for partially coherently superposed states. Phys. Rev. A 93(3), 032331 (2016)
Zhu, X.N., Fei, S.M.: General monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf. Process. 16(2), 53 (2017)
Jin, Z.X., Fei, S.M.: Tighter monogamy relations of quantum entanglement for multiqubit W-class states. Quantum Inf. Process. 17(1), 2 (2018)
Uhlmann, A.: Fidelity and concurrence of conjugated states. Phys. Rev. A 62(3), 032307 (2000)
Lee, S., Chi, D.P., Oh, S.D., Kim, J.: Convex-roof extended negativity as an entanglement measure for bipartite quantum systems. Phys. Rev. A 68(6), 062304 (2003)
Horodecki, P.: Separability criterion and inseparable mixed states with positive partial transposition. Phys. Lett. A 232(3), 333–339 (1997)
Dür, W., Cirac, J., Lewenstein, M., Bruß, D.: Distillability and partial transposition in bipartite systems. Phys. Rev. A 61(6), 062313 (2000)
Audenaert, K.M.: Subadditivity of \(q\)-entropies for q \(\ge 1\). J. Math. Phys. 48(8), 083507 (2007)
Agrawal, P., Pati, A.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74(6), 062320 (2006)
shui Yu, C., shan Song, H.: Measurable entanglement for tripartite quantum pure states of qubits. Phys. Rev. A 76(2), 022324 (2007)
Jin, Z.X., Li, J., Li, T., Fei, S.M.: Tighter monogamy relations in multiqubit systems. Phys. Rev. A 97(3), 032336 (2018)
Briegel, H.J., Raussendorf, R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86(5), 910 (2001)
Humphreys, P.C., Barbieri, M., Datta, A., Walmsley, I.A.: Quantum enhanced multiple phase estimation. Phys. Rev. Lett. 111(7), 070403 (2013)
Liu, J., Lu, X.M., Sun, Z., Wang, X.: Quantum multiparameter metrology with generalized entangled coherent state. J. Phys. A: Math. Theor. 49(11), 115302 (2016)
Acknowledgements
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].
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Khan, A., Farooq, A., Jeong, Y. et al. Distribution of entanglement in multipartite systems. Quantum Inf Process 18, 60 (2019). https://doi.org/10.1007/s11128-019-2178-9
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DOI: https://doi.org/10.1007/s11128-019-2178-9