Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

doi:10.1088/1674-1056/ab7dab

中国物理B ›› 2020, Vol. 29 ›› Issue (5): 50302-050302.doi: 10.1088/1674-1056/ab7dab

• SPECIAL TOPIC—Recent advances in thermoelectric materials and devices • 上一篇下一篇

Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

Shao-Xiong Wu(武少雄), Chang-Shui Yu(于长水)

1 School of Science, North University of China, Taiyuan 030051, China;
2 School of Physics, Dalian University of Technology, Dalian 116024, China

收稿日期:2020-02-12 修回日期:2020-03-01 出版日期:2020-05-05 发布日期:2020-05-05
通讯作者: Shao-Xiong Wu, Chang-Shui Yu E-mail:sxwu@nuc.edu.cn;ycs@dlut.edu.cn
基金资助:
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).

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

Received:2020-02-12 Revised:2020-03-01 Online:2020-05-05 Published:2020-05-05
Contact: Shao-Xiong Wu, Chang-Shui Yu E-mail:sxwu@nuc.edu.cn;ycs@dlut.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: quantum speed limit, Wigner function, phase space, Margolus-Levitin bound

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.

Key words: quantum speed limit, Wigner function, phase space, Margolus-Levitin bound

中图分类号: (Quantum mechanics)

03.65.-w

03.65.Db (Functional analytical methods) 03.67.-a (Quantum information)

武少雄, 于长水. Margolus-Levitin speed limit across quantum to classical regimes based on trace distance[J]. 中国物理B, 2020, 29(5): 50302-050302.

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[J]. Chin. Phys. B, 2020, 29(5): 50302-050302.

参考文献 59

[1]	Mandelstam L and Tamm I 1945 J. Phys. (USSR) 9 249
[2]	Margolus N and Levitin L B 1998 Physica D 120 188 doi: 10.1016/S0167-2789(98)00054-2
[3]	Levitin L B and Toffoli T 2009 Phys. Rev. Lett. 103 160502 doi: 10.1103/PhysRevLett.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 doi: 10.1103/PhysRevLett.103.240501
[5]	Bekenstein J D 1981 Phys. Rev. Lett. 46 623 doi: 10.1103/PhysRevLett.46.623
[6]	Fleming G N 1973 Nuovo Cimento 16 232 doi: 10.1007/BF02819419
[7]	Bhattacharyya K 1983 J. Phys. A 16 2993 doi: 10.1088/0305-4470/16/13/021
[8]	Anandan J and Aharonov Y 1990 Phys. Rev. Lett. 65 1697 doi: 10.1103/PhysRevLett.65.1697
[9]	Pati A K 1991 Phys. Lett. A 159 105 doi: 10.1016/0375-9601(91)90255-7
[10]	Vaidman L 1992 Am. J. Phys. 60 182 doi: 10.1119/1.16940
[11]	Brody D C 2003 J. Phys. A: Math. Gen. 36 5587 doi: 10.1088/0305-4470/36/20/314
[12]	Jones P J and Kok P 2010 Phys. Rev. A 82 022107 doi: 10.1103/PhysRevA.82.022107
[13]	Campaioli F, Pollock F A, Binder F C and Modi K 2018 Phys. Rev. Lett. 120 060409 doi: 10.1103/PhysRevLett.120.060409
[14]	Taddei M M, Escher B M, Davidovich L and de Matos Filho R L 2013 Phys. Rev. Lett. 110 050402 doi: 10.1103/PhysRevLett.110.050402
[15]	del Campo A, Egusquiza I L, Plenio M B and Huelga S F 2013 Phys. Rev. Lett. 110 050403 doi: 10.1103/PhysRevLett.110.050403
[16]	Deffner S and Lutz E 2013 Phys. Rev. Lett. 111 010402 doi: 10.1103/PhysRevLett.111.010402
[17]	Xu Z Y, Luo S, Yang W L, Liu C and Zhu S 2014 Phys. Rev. A 89 012307 doi: 10.1103/PhysRevA.89.012307
[18]	Zhang Y J, Han W, Xia Y J, Cao J P and Fan H 2015 Sci. Rep. 4 4890 doi: 10.1038/srep04890
[19]	Xu Z Y and Zhu S Q 2014 Chin. Phys. Lett. 31 020301 doi: 10.1088/0256-307X/31/2/020301
[20]	Wu S X, Zhang Y, Yu C S and Song H S 2015 J. Phys. A: Math. Theor. 48 045301 doi: 10.1088/1751-8113/48/4/045301
[21]	Sun Z, Liu J, Ma J and Wang X 2015 Sci. Reps. 5 8444 doi: 10.1038/srep08444
[22]	Zhang Y J, Xia Y J and Fan H 2016 Europhys. Lett. 116 30001 doi: 10.1209/0295-5075/116/30001
[23]	Jing J, Wu L A and del Campo A 2016 Sci. Rep. 6 38149 doi: 10.1038/srep38149
[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 doi: 10.1088/1674-1056/25/8/080304
[26]	Mondal D, Datta C and Sazim S 2016 Phys. Lett. A 380 689 doi: 10.1016/j.physleta.2015.12.015
[27]	Deffner S 2017 New J. Phys. 19 103018 doi: 10.1088/1367-2630/aa83dc
[28]	Cai X and Zheng Y 2017 Phys. Rev. A 95 052104 doi: 10.1103/PhysRevA.95.052104
[29]	Hou L, Shao B, Wei Y and Zou J 2017 Eur. Phys. J. D 71 22 doi: 10.1140/epjd/e2016-70460-6
[30]	Campbell S and Deffner S 2017 Phys. Rev. Lett. 118 100601 doi: 10.1103/PhysRevLett.118.100601
[31]	Wu S X and Yu C S 2018 Phys. Rev. A 98 042132 doi: 10.1103/PhysRevA.98.042132
[32]	Yu M, Fang M F and Zou H M 2018 Chin. Phys. B 27 010303 doi: 10.1088/1674-1056/27/1/010303
[33]	Zhang L, Sun Y and Luo S 2018 Phys. Lett. A 382 2599 doi: 10.1016/j.physleta.2018.07.030
[34]	Xu Z Y, You W L, Dong Y L, Zhang C and Yang W L 2018 Phys. Rev. A 97 032115 doi: 10.1103/PhysRevA.97.032115
[35]	Liu J, Sega D and Hanna G 2019 J. Phys. A: Math. Theor. 52 215301 doi: 10.1088/1751-8121/ab15eb
[36]	Teittinen J, Lyyra H and Maniscalco S 2019 New J. Phys. 21 123041 doi: 10.1088/1367-2630/ab59fe
[37]	Funo K, Shiraishi N and Saito K 2019 New J. Phys. 21 013006 doi: 10.1088/1367-2630/aaf9f5
[38]	Xu K, Zhang G F and Liu W M 2019 Phys. Rev. A 100 052305 doi: 10.1103/PhysRevA.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 doi: 10.1088/1674-1056/ab6c45
[41]	García-Pintos L P and del Campo A 2019 New J. Phys. 21 033012 doi: 10.1088/1367-2630/ab099e
[42]	Haseli S 2019 Eur. Phys. J. C 79 616 doi: 10.1140/epjc/s10052-019-7129-1
[43]	Sun S and Zheng Y 2019 Phys. Rev. Lett. 123 180403 doi: 10.1103/PhysRevLett.123.180403
[44]	Deffner S and Campbell S 2017 J. Phys. A: Math. Theor. 50 453001 doi: 10.1088/1751-8121/aa86c6
[45]	Shanahan B, Chenu A, Margolus N and del Campo A 2018 Phys. Rev. Lett. 120 070401 doi: 10.1103/PhysRevLett.120.070401
[46]	Okuyama M and Ohzeki M 2018 Phys. Rev. Lett. 120 070402 doi: 10.1103/PhysRevLett.120.070402
[47]	Hillery M, O'Connell R F, Scully M O and Wigner E P 1984 Phys. Rep. 106 121 doi: 10.1016/0370-1573(84)90160-1
[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 doi: 10.1103/PhysRevLett.109.190403
[50]	Bondar D I, Cabrera R, Zhdanov D V and Rabitz H A 2013 Phys. Rev. A 88 052108 doi: 10.1103/PhysRevA.88.052108
[51]	Bhattacharyya A 1946 Indian J. Stat. 7 401
[52]	Chang L and Luo S 2013 Phys. Rev. A 87 062303 doi: 10.1103/PhysRevA.87.062303
[53]	Girolami D, Tufarelli T and Adesso G 2013 Phys. Rev. Lett. 110 240402 doi: 10.1103/PhysRevLett.110.240402
[54]	Wu S X, Zhang J, Yu C S and Song H S 2014 Phys. Lett. A 378 344 doi: 10.1016/j.physleta.2013.11.047
[55]	Chen X and Muga J G 2010 Phys. Rev. A 82 053403 doi: 10.1103/PhysRevA.82.053403
[56]	del Campo A, Goold J and Paternostro M 2015 Sci. Rep. 4 6208 doi: 10.1038/srep06208
[57]	Chen X, Ruschhaupt A, Schmidt S, del Campo A, Guéry-Odelin D and Muga J G 2010 Phys. Rev. Lett. 104 063002 doi: 10.1103/PhysRevLett.104.063002
[58]	Ozawa M 2000 Phys. Lett. A 268 158 doi: 10.1016/S0375-9601(00)00171-7
[59]	Piani M 2012 Phys. Rev. A 86 034101 doi: 10.1103/PhysRevA.86.034101

Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

Margolus-Levitin speed limit across quantum to classical regimes based on trace distance

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