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Entanglement is a vital resource for many quantum information processes. However, the unavoidable interaction between quantum system and its environment will lead to quantum decoherence. So protecting remote entanglement against decoherence is of great importance for realizing quantum information and quantum communication. In fact, there are many types of decoherences. Besides the depolarization and phase damping, amplitude damping is a typical decoherence mechanism. If we monitor the environments to guarantee that no excitation escapes from the system, the amplitude damping is modified into a weak measurement induced amplitude damping of the system. Amplitude damping decoherence can affect both single-qubit quantum states and multipartite entangled states. However, in most of previous quantum state protection schemes, the authors only pay attention to the single-qubit system or two-qubit system. Compared with bipartite entangled states, multipartite entangled states possess many advantages, but the entanglement property of multipartite entangled state is much more complicated than bipartite entanglement, so bipartite entanglement reversal (protection) scheme may not be suitable for multipartite case. Thus, in this paper, according to local pulse series and weak measurement, we propose an effective scheme for protecting two multipartite entangled states against amplitude damping, and these two multipartite states are Cluster state and Maximal slice (MS) state. Cluster state and MS state are two typical classes of multipartite entangled states, which play important roles in quantum computation and communication, respectively. These two states cannot be converted into each other with local operation and classical communication. Owing to its good operational and computable properties, here we choose negativity as a measure to quantify the multipartite entanglement. For the case of MS sate, no matter what the initial parameter is, when the local pulses are exerted on all qubits, the entanglement can be fixed around the entanglement of the initial state. Similarly, in the four-qubit cluster state case, if a series of flip operations is exerted on all qubits, it is shown that the multipartite entanglement can be recovered to the maximum 1.0. All these results show that this protocol can protect remote multipartite entanglement effectively. The physical mechanism behind this scheme is that the weak measurement combining with flip operation can balance the weight of different terms of the state, and move the entanglement toward the initial value. To summarize, our scheme is much simpler and feasible, which may warrant its experimental realization. Moreover, our scheme could be extended to protect other multipartite states.
[1] Xue Z Y, Zhou J, Wang Z D 2015 Phys. Rev. A 92 022320
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[22] Liao X P, Fang M F, Fang J S, Zhu Q Q 2014 Chin. Phys. B 23 020304
[23] Wang M J, Xia Y J 2015 Phys. Sin. 64 40303
[24] Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys 58 1131
[25] Dr W 2001 Phys. Rev. A 63 020303
[26] Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910
[27] Gao T, Yan F L, Li Y C 2008 Eur. Phys. Lett. 84 50001
[28] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 430 54
[29] Kempe J 1999 Phys. Rev. A 60 910
[30] Wang J, Zhang Q, Tang C J 2007 Commun. Theor. Phys. 48 637
[31] Menicucci N C, Loock P V, Gu M, Weedbrook C, Ralph T C, Nielsen M A 2006 Phys. Rev. Lett. 97 110501
[32] Ukai R, Iwata N, Shimokawa Y, Armstrong S C, Politi A, Yoshikawa J, van Peter L, Furusawa A 2011 Phys. Rev. Lett. 106 240504
[33] Vidal G, Werner R F 2002 Phys. Rev. A 65 032314
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[1] Xue Z Y, Zhou J, Wang Z D 2015 Phys. Rev. A 92 022320
[2] Masanes L, Pironio S, Acn A 2011 Nat. Commun. 2 238
[3] Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[4] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
[5] Kim Y H, Kulik S P, Shih Y 2001 Phys. Rev. Lett. 86 1370
[6] Giovannetti V, Lloyd S, Maccone L 2011 Nature Photon. 5 222
[7] Xue Z Y 2010 J. Anhui Univ. 34 12
[8] Steane A M 1996 Phys. Rev. Lett. 77 793
[9] Lidar D A, Chuang I L, Whaley K B 1998 Phys. Rev. Lett. 81 2594
[10] Kwiat P G, Berglund A J, Altepeter J B, White A G 2000 Science 290 498
[11] Facchi P, Lidar D A, Pascazio S 2004 Phys. Rev. A 69 183
[12] Maniscalco S, Francica F, Zaffino R L, Zaffino R L, Gullo N L, Plastina F 2008 Phys. Rev. Lett. 100 1937
[13] Sun Q H, Yang M, Cao Z L 2011 J. Anhui Univ. 35 34
[14] Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 82 2417
[15] Koashi M, Ueda M 1999 Phys. Rev. Lett. 82 2598
[16] Korotkov A N, Jordan A N 2006 Phys. Rev. Lett. 97 166805
[17] Katz N 2008 Phys. Rev. Lett. 101 200401
[18] Kim Y S, Cho Y W, Ra Y S, Kim Y H 2009 Opt. Express 17 11978
[19] Sun Q, Al-Amri M, Zubairy M S 2009 Phys. Rev. A 80 033838
[20] Sun Q, Al-Amri M, Davidovich L, Zubairy M S 2010 Phys. Rev. A 82 052323
[21] Kim Y S, Lee J C, Kwon O, Kim Y H 2012 Nature Phys. 8 117
[22] Liao X P, Fang M F, Fang J S, Zhu Q Q 2014 Chin. Phys. B 23 020304
[23] Wang M J, Xia Y J 2015 Phys. Sin. 64 40303
[24] Greenberger D M, Horne M A, Shimony A, Zeilinger A 1990 Am. J. Phys 58 1131
[25] Dr W 2001 Phys. Rev. A 63 020303
[26] Briegel H J, Raussendorf R 2001 Phys. Rev. Lett. 86 910
[27] Gao T, Yan F L, Li Y C 2008 Eur. Phys. Lett. 84 50001
[28] Zhao Z, Chen Y A, Zhang A N, Yang T, Briegel H J, Pan J W 2004 Nature 430 54
[29] Kempe J 1999 Phys. Rev. A 60 910
[30] Wang J, Zhang Q, Tang C J 2007 Commun. Theor. Phys. 48 637
[31] Menicucci N C, Loock P V, Gu M, Weedbrook C, Ralph T C, Nielsen M A 2006 Phys. Rev. Lett. 97 110501
[32] Ukai R, Iwata N, Shimokawa Y, Armstrong S C, Politi A, Yoshikawa J, van Peter L, Furusawa A 2011 Phys. Rev. Lett. 106 240504
[33] Vidal G, Werner R F 2002 Phys. Rev. A 65 032314
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