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Chin. Phys. B, 2020, Vol. 29(5): 050302    DOI: 10.1088/1674-1056/ab7dab
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Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

Shao-Xiong Wu(武少雄)1, Chang-Shui Yu(于长水)2
1 School of Science, North University of China, Taiyuan 030051, China;
2 School of Physics, Dalian University of Technology, Dalian 116024, China
Abstract  The classical version of Mandelstam-Tamm speed limit based on the Wigner function in phase space was reported by Shanahan et al. [Phys. Rev. Lett. 120 070401 (2018)]. We present the Margolus-Levitin speed limit across the quantum-to-classical transition in phase space based on the trace distance. The Margolus-Levitin speed limit is set by the Schatten L1 norm of the generator of time-dependent evolution for both the quantum and classical domains. As an example, the time-dependent harmonic oscillator is considered to illustrate the result.
Keywords:  quantum speed limit      Wigner function      phase space      Margolus-Levitin bound  
Received:  12 February 2020      Revised:  01 March 2020      Accepted manuscript online: 
PACS:  03.65.-w (Quantum mechanics)  
  03.65.Db (Functional analytical methods)  
  03.67.-a (Quantum information)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11775040), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province of China (Grant No. 2019L0527), and the Fundamental Research Fund for the Central Universities of China (Grant No. DUT18LK45).
Corresponding Authors:  Shao-Xiong Wu, Chang-Shui Yu     E-mail:  sxwu@nuc.edu.cn;ycs@dlut.edu.cn

Cite this article: 

Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水) Margolus-Levitin speed limit across quantum to classical regimes based on trace distance 2020 Chin. Phys. B 29 050302

[1] Mandelstam L and Tamm I 1945 J. Phys. (USSR) 9 249
[2] Margolus N and Levitin L B 1998 Physica D 120 188
[3] Levitin L B and Toffoli T 2009 Phys. Rev. Lett. 103 160502
[4] Caneva T, Murphy M, Calarco T, Fazio R, Montangero S, Giovannetti V and Santoro G E 2009 Phys. Rev. Lett. 103 240501
[5] Bekenstein J D 1981 Phys. Rev. Lett. 46 623
[6] Fleming G N 1973 Nuovo Cimento 16 232
[7] Bhattacharyya K 1983 J. Phys. A 16 2993
[8] Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697
[9] Pati A K 1991 Phys. Lett. A 159 105
[10] Vaidman L 1992 Am. J. Phys. 60 182
[11] Brody D C 2003 J. Phys. A: Math. Gen. 36 5587
[12] Jones P J and Kok P 2010 Phys. Rev. A 82 022107
[13] Campaioli F, Pollock F A, Binder F C and Modi K 2018 Phys. Rev. Lett. 120 060409
[14] Taddei M M, Escher B M, Davidovich L and de Matos Filho R L 2013 Phys. Rev. Lett. 110 050402
[15] del Campo A, Egusquiza I L, Plenio M B and Huelga S F 2013 Phys. Rev. Lett. 110 050403
[16] Deffner S and Lutz E 2013 Phys. Rev. Lett. 111 010402
[17] Xu Z Y, Luo S, Yang W L, Liu C and Zhu S 2014 Phys. Rev. A 89 012307
[18] Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Sci. Rep. 4 4890
[19] Xu Z Y and Zhu S Q 2014 Chin. Phys. Lett. 31 020301
[20] Wu S X, Zhang Y, Yu C S and Song H S 2015 J. Phys. A: Math. Theor. 48 045301
[21] Sun Z, Liu J, Ma J and Wang X 2015 Sci. Reps. 5 8444
[22] Zhang Y J, Xia Y J and Fan H 2016 Europhys. Lett. 116 30001
[23] Jing J, Wu L A and del Campo A 2016 Sci. Rep. 6 38149
[24] Pires D P, Cianciaruso M, Céleri L C, Adesso G and Soares-Pinto D O 2016 Phys. Rev. X 6 021031
[25] He Z, Yao C M, Li L and Wang Q 2016 Chin. Phys. B 25 080304
[26] Mondal D, Datta C and Sazim S 2016 Phys. Lett. A 380 689
[27] Deffner S 2017 New J. Phys. 19 103018
[28] Cai X and Zheng Y 2017 Phys. Rev. A 95 052104
[29] Hou L, Shao B, Wei Y and Zou J 2017 Eur. Phys. J. D 71 22
[30] Campbell S and Deffner S 2017 Phys. Rev. Lett. 118 100601
[31] Wu S X and Yu C S 2018 Phys. Rev. A 98 042132
[32] Yu M, Fang M F and Zou H M 2018 Chin. Phys. B 27 010303
[33] Zhang L, Sun Y and Luo S 2018 Phys. Lett. A 382 2599
[34] Xu Z Y, You W L, Dong Y L, Zhang C and Yang W L 2018 Phys. Rev. A 97 032115
[35] Liu J, Sega D and Hanna G 2019 J. Phys. A: Math. Theor. 52 215301
[36] Teittinen J, Lyyra H and Maniscalco S 2019 New J. Phys. 21 123041
[37] Funo K, Shiraishi N and Saito K 2019 New J. Phys. 21 013006
[38] Xu K, Zhang G F and Liu W M 2019 Phys. Rev. A 100 052305
[39] Feng H R, Li P and Yue X F 2019 Acta Phys. Sin. 68 050201 (in Chinese)
[40] Wang Y Y and Fang M F 2020 Chin. Phys. B 29 030304
[41] García-Pintos L P and del Campo A 2019 New J. Phys. 21 033012
[42] Haseli S 2019 Eur. Phys. J. C 79 616
[43] Sun S and Zheng Y 2019 Phys. Rev. Lett. 123 180403
[44] Deffner S and Campbell S 2017 J. Phys. A: Math. Theor. 50 453001
[45] Shanahan B, Chenu A, Margolus N and del Campo A 2018 Phys. Rev. Lett. 120 070401
[46] Okuyama M and Ohzeki M 2018 Phys. Rev. Lett. 120 070402
[47] Hillery M, O'Connell R F, Scully M O and Wigner E P 1984 Phys. Rep. 106 121
[48] Zachos C K, Fairlie D B and Curtright T L 2005 Quantum mechnics in the phase space: an overview with selected papers (Singapore: World Scientific)
[49] Bondar D I, Cabrera R, Lompay R R, Ivanov M Y and Rabitz H A 2012 Phys. Rev. Lett. 109 190403
[50] Bondar D I, Cabrera R, Zhdanov D V and Rabitz H A 2013 Phys. Rev. A 88 052108
[51] Bhattacharyya A 1946 Indian J. Stat. 7 401
[52] Chang L and Luo S 2013 Phys. Rev. A 87 062303
[53] Girolami D, Tufarelli T and Adesso G 2013 Phys. Rev. Lett. 110 240402
[54] Wu S X, Zhang J, Yu C S and Song H S 2014 Phys. Lett. A 378 344
[55] Chen X and Muga J G 2010 Phys. Rev. A 82 053403
[56] del Campo A, Goold J and Paternostro M 2015 Sci. Rep. 4 6208
[57] Chen X, Ruschhaupt A, Schmidt S, del Campo A, Guéry-Odelin D and Muga J G 2010 Phys. Rev. Lett. 104 063002
[58] Ozawa M 2000 Phys. Lett. A 268 158
[59] Piani M 2012 Phys. Rev. A 86 034101
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