Qubit movement-assisted entanglement swapping

doi:10.1088/1674-1056/ab7da3

摘要/Abstract

摘要： We propose a scheme to generate entanglement between two distant qubits (two-level atom) which are separately trapped in their own (in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement. It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement (Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.

关键词: dissipative systems, quantum entanglement, entanglement swapping

Abstract: We propose a scheme to generate entanglement between two distant qubits (two-level atom) which are separately trapped in their own (in general) non-Markovian dissipative cavities by utilizing entangling swapping, considering the case in which the qubits can move along their cavity axes rather than a static state of motion. We first examine the role of movement of the qubit by studying the entropy evolution for each subsystem. The average entropy over the initial states of the qubit is calculated. Then by performing a Bell state measurement on the fields leaving the cavities, we swap the entanglement between qubit-field in each cavity into qubit-qubit and field-field subsystems. The entangling power is used to measure the average amount of swapped entanglement over all possible pure initial states. Our results are presented in two weak and strong coupling regimes, illustrating the positive role of movement of the qubits on the swapped entanglement. It is revealed that by considering certain conditions for the initial state of qubits, it is possible to achieve a maximally long-leaving stationary entanglement (Bell state) which is entirely independent of the environmental variables as well as the velocity of qubits. This happens when the two qubits have the same velocities.

Key words: dissipative systems, quantum entanglement, entanglement swapping

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

03.65.Ud (Entanglement and quantum nonlocality) 03.67.Mn (Entanglement measures, witnesses, and other characterizations)

Sare Golkar, Mohammad Kazem Tavassoly, Alireza Nourmandipour. Qubit movement-assisted entanglement swapping[J]. 中国物理B, 2020, 29(5): 50304-050304.

Sare Golkar, Mohammad Kazem Tavassoly, Alireza Nourmandipour. Qubit movement-assisted entanglement swapping[J]. Chin. Phys. B, 2020, 29(5): 50304-050304.

参考文献 74

[1]	Horodecki R, Horodecki P, Horodecki M and Horodecki K 2009 Rev. Mod. Phys. 81 865 doi: 10.1103/RevModPhys.81.865
[2]	Braunstein S L and Mann A 1995 Phys. Rev. A. 51 R1727(R)
[3]	Zhang S L, Jin C H, Shi J H, Guo J S, Zou X B and Guo G C 2017 Chin. Phys. Lett. 34 040302 doi: 10.1088/0256-307X/34/4/040302
[4]	Ekert A K 1991 Phys. Rev. Lett. 67 661 doi: 10.1103/PhysRevLett.67.661
[5]	Richter T and Vogel W 2007 Phys. Rev. A 76 053835 doi: 10.1103/PhysRevA.76.053835
[6]	Murao M, Jonathan D, Plenio M B and Vedral V 1999 Phys. Rev. A 59 156 doi: 10.1103/PhysRevA.59.156
[7]	Koike S, Takahashi H, Yonezawa H, Takei N, Braunstein S L, Aoki T and Furusawa A 2006 Phys. Rev. Lett. 96 060504 doi: 10.1103/PhysRevLett.96.060504
[8]	Mattle K, Weinfurter H, Kwiat P G and Zeilinger A 1996 Phys. Rev. Lett. 76 4656 doi: 10.1103/PhysRevLett.76.4656
[9]	Raimond J M, Brune M and Haroche S 2001 Rev. Mod. Phys. 73 565 doi: 10.1103/RevModPhys.73.565
[10]	Pazy E, Biolatti E, Calarco T, D Amico I, Zanardi P, Rossi F and Zoller P 2003 Europhys. Lett. 62 175 doi: 10.1209/epl/i2003-00343-4
[11]	Julsgaard B, Kozhekin A and Polzik E S 2001 Nature 413 400 doi: 10.1038/35096524
[12]	Yang C P, Chu S I and Han S 2003 Phys. Rev. A 67 042311 doi: 10.1103/PhysRevA.67.042311
[13]	Yang C P, Chu S I and Han S 2004 Phys. Rev. Lett. 92 117902 doi: 10.1103/PhysRevLett.92.117902
[14]	Aspect A, Grangier P and Roger G 1981 Phys. Rev. Lett. 47 460 doi: 10.1103/PhysRevLett.47.460
[15]	Izmalkov A, Grajcar M, Il'ichev E, Wagner Th, Meyer H G, Yu A, Amin M H S, van den Brink A M and Zagoskin A M 2004 Phys. Rev. Lett. 93 037003 doi: 10.1103/PhysRevLett.93.037003
[16]	Pachos J and Walther H 2002 Phys. Rev. Lett. 89 187903 doi: 10.1103/PhysRevLett.89.187903
[17]	Cirac J I and Zoller P 1995 Phys. Rev. Lett. 74 4091 doi: 10.1103/PhysRevLett.74.4091
[18]	Sackett C A, Kielpinski D, King B E, Langer C, Meyer V, Myatt C J, Rowe M, Turchette Q A, Itano W M, Wineland D J and Monroe C 2000 Nature 404 256 doi: 10.1038/35005011
[19]	Jaynes E T and Cummings F W 1963 Proc. IEEE 51 89 doi: 10.1109/PROC.1963.1664
[20]	Tavis M and Cummings F W 1968 Phys. Rev. 170 379 doi: 10.1103/PhysRev.170.379
[21]	Żukowski M, Zeilinger A, Horne M A and Ekert A K 1993 Phys. Rev. Lett. 71 4287 doi: 10.1103/PhysRevLett.71.4287
[22]	Pakniat R, Tavassoly M K and Zandi M H 2016 Chin. Phys. B 25 100303 doi: 10.1088/1674-1056/25/10/100303
[23]	Polkinghorne R E S and Ralph T C 1999 Phys. Rev. Lett. 83 2095 doi: 10.1103/PhysRevLett.83.2095
[24]	Bose S, Vedral V and Knight P L 1998 Phys. Rev. A 57 822 doi: 10.1103/PhysRevA.57.822
[25]	Jia X, Su X, Pan Q, Gao J, Xie C and Peng K 2004 Phys. Rev. Lett. 93 250503 doi: 10.1103/PhysRevLett.93.250503
[26]	Hu C Y and Rarity J G 2011 Phys. Rev. B 83 115303 doi: 10.1103/PhysRevB.83.115303
[27]	Shi B S, Jiang Y K and Guo G C 2000 Phys. Rev. A 62 054301 doi: 10.1103/PhysRevA.62.054301
[28]	de Almeida N G 2015 J. Phys. B: At. Mol. Opt. Phys. 48 115508 doi: 10.1088/0953-4075/48/11/115508
[29]	Ghasemi M, Tavassoly M K and Nourmandipour A 2017 Eur. Phys. J. Plus 132 531 doi: 10.1140/epjp/i2017-11815-y
[30]	Ning W, Huang X J, Han P R, Li H, Deng H, Yang Z B, Zhong Z R, Xia Y, Xu K, Zheng D and Zheng S B 2019 Phys. Rev. Lett. 123 060502 doi: 10.1103/PhysRevLett.123.060502
[31]	Zopf M, Keil R, Chen Y, Yang J, Chen D, Ding F and Schmidt O G 2019 Phys. Rev. Lett. 123 160502 doi: 10.1103/PhysRevLett.123.160502
[32]	Yu T and Eberly J H 2003 Phys. Rev. B 68 165322 doi: 10.1103/PhysRevB.68.165322
[33]	Yu T and Eberly J H 2004 Phys. Rev. Lett. 93 140404 doi: 10.1103/PhysRevLett.93.140404
[34]	Nourmandipour A and Tavassoly M K 2015 Eur. Phys. J. Plus 130 148 doi: 10.1140/epjp/i2015-15148-7
[35]	Mortezapour A, Abedi M, Mahmoudi M and Khajehpour M R H 2011 J. Phys. B: At. Mol. Opt. Phys. 44 085501 doi: 10.1088/0953-4075/44/8/085501
[36]	Kim Y S, Lee J C, Kwon O and Kim Y H 2012 Nat. Phys. 8 117 doi: 10.1038/nphys2178
[37]	Rafiee M, Nourmandipour A and Mancini S 2016 Phys. Rev. A 94 012310 doi: 10.1103/PhysRevA.94.012310
[38]	Rafiee M, Nourmandipour A and Mancini S 2017 Phys. Rev. A 96 012340 doi: 10.1103/PhysRevA.96.012340
[39]	Mortezapour A, Naeimi G and Lo Franco R 2018 Opt. Commun. 424 26 doi: 10.1016/j.optcom.2018.04.044
[40]	Mortezapour A and Lo Franco R 2018 Sci. Rep. 8 14304 doi: 10.1038/s41598-018-32661-2
[41]	Zhang D J, Liu C L and Tong D M 2015 Chin. Phys. Lett. 32 40302 doi: 10.1088/0256-307X/32/4/040302
[42]	Hu J and Xue Q 2019 Chin. Phys. B 28 070303 doi: 10.1088/1674-1056/28/7/070303
[43]	Nourmandipour A and Tavassoly M K 2015 J. Phys. B: At. Mol. Opt. Phys. 48 165502 doi: 10.1088/0953-4075/48/16/165502
[44]	Maniscalco S, Francica F, Zaffino R L, Lo Gullo N and Plastina F 2008 Phys. Rev. Lett. 100 090503 doi: 10.1103/PhysRevLett.100.090503
[45]	Huang L Y and Fang M F 2010 Chin. Phys. B 19 090318 doi: 10.1088/1674-1056/19/9/090318
[46]	Wang X L, Ren Y K and Zeng H S 2019 Chin. Phys. B 28 030301 doi: 10.1088/1674-1056/28/3/030301
[47]	Wang M J and Xia Y J 2019 Chin. Phys. B 28 060303 doi: 10.1088/1674-1056/28/6/060303
[48]	Nourmandipour A, Tavassoly M K and Rafiee M 2016 Phys. Rev. A 93 022327 doi: 10.1103/PhysRevA.93.022327
[49]	Nourmandipour A, Tavassoly M K and Bolorizadeh M A 2016 J. Opt. Soc. Am. B 33 1723
[50]	Shankar A, Lakshmibala S and Balakrishnan V 2014 J. Phys. B: At. Mol. Opt. Phys. 47 215505 doi: 10.1088/0953-4075/47/21/215505
[51]	Schirmer S G and Wang X 2010 Phys. Rev. A 81 062306 doi: 10.1103/PhysRevA.81.062306
[52]	Didier N, Guillaud J, Shankar S and Mirrahimi M 2018 Phys. Rev. A 98 012329 doi: 10.1103/PhysRevA.98.012329
[53]	Xiao X, Fang M F and Li Y L 2010 J. Phys. B: At. Mol. Opt. Phys. 43 185505 doi: 10.1088/0953-4075/43/18/185505
[54]	Haikka P and Maniscalco S 2010 Phys. Rev. A 81 052103 doi: 10.1103/PhysRevA.81.052103
[55]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Phys. Rev. A 91 032112 doi: 10.1103/PhysRevA.91.032112
[56]	Ren Y K, Tang L M and Zeng H S 2016 Quantum Inf. Process. 15 5011 doi: 10.1007/s11128-016-1444-3
[57]	Mortezapour A, Borji M A and Lo Franco R 2017 Laser Phys. Lett. 14 055201 doi: 10.1088/1612-202X/aa63c5
[58]	Calajó G and Rabl P 2017 Phys. Rev. A 95 043824 doi: 10.1103/PhysRevA.95.043824
[59]	García-Álvarez L, Felicetti S, Rico E, Solano E and Sabín C 2017 Sci. Rep. 7 657 doi: 10.1038/s41598-017-00770-z
[60]	Felicetti S, Sabín C, Fuentes I, Lamata L, Romero G and Solano E 2015 Phys. Rev. B 92 064501 doi: 10.1103/PhysRevB.92.064501
[61]	Moustos D and Anastopoulos C 2017 Phys. Rev. D 95 025020 doi: 10.1103/PhysRevD.95.025020
[62]	Golkar S, Tavassoly M K and Nourmandipour A 2020 J. Opt. Soc. Am. B 37 400 doi: 10.1364/JOSAB.379261
[63]	Wootters K 1998 Phys. Rev. Lett. 80 2245 doi: 10.1103/PhysRevLett.80.2245
[64]	Zanardi P, Zalka C and Faoro L 2000 Phys. Rev. A 62 030301 doi: 10.1103/PhysRevA.62.030301
[65]	Nourmandipour A, Tavassoly M K and Mancini S 2016 Quantum Inf. Comput. 16 969
[66]	Asbóth J K, Domokos P and Ritsch H 2004 Phys. Rev. A 70 013414 doi: 10.1103/PhysRevA.70.013414
[67]	Katsuki H, Delagnes J C, Hosaka K et al. 2013 Nat. Commun. 4 2801 doi: 10.1038/ncomms3801
[68]	Park D 2017 arXiv:1703.09341 [quant-ph]
[69]	Peters N A, Wei T C and Kwiat P G 2004 Phys. Rev. A 70 052309 doi: 10.1103/PhysRevA.70.052309
[70]	Eghbali-Arani M, Yavari H, Shahzamanian M A, Giovannetti V and Barzanjeh S 2015 J. Opt. Soc. Am. B 32 798 doi: 10.1364/JOSAB.32.000798
[71]	Lee S W and Jeong H 2013 arXiv:1304.1214 [quant-ph]
[72]	Nourmandipour A and Tavassoly M K 2016 Phys. Rev. A 94 022339 doi: 10.1103/PhysRevA.94.022339
[73]	Mortezapour A, Nourmandipour A and Gholipour H 2020 Quantum Inf. Process. 19 136 doi: 10.1007/s11128-020-02634-4
[74]	Briegel H J, Dür, Cirac J I and Zoller P 1998 Phys. Rev. Lett. 81 5932 doi: 10.1103/PhysRevLett.81.5932