A Hierarchy in Majorana Non-Abelian Tests and Hidden Variable Models
-
Abstract
The recent progress of the Majorana experiments paves a way for the future tests of non-Abelian braiding statistics and topologically protected quantum information processing. However, a deficient design in those tests could be very dangerous and reach false-positive conclusions. A careful theoretical analysis is necessary so as to develop loophole-free tests. We introduce a series of classical hidden variable models to capture certain key properties of Majorana system: non-locality, topologically non-triviality, and quantum interference. Those models could help us to classify the Majorana properties and to set up the boundaries and limitations of Majorana non-Abelian tests: fusion tests, braiding tests and test set with joint measurements. We find a hierarchy among those Majorana tests with increasing experimental complexity. -
Acknowledgement: This work was supported by the National Natural Science Foundation of China (Grant No. 11974198), the Innovation Program for Quantum Science and Technology (Grant No. 2021ZD0302400), and the Tsinghua University Initiative Scientific Research Program.
-
References
[1] Kitaev A Y 2003 Ann. Phys. 303 2 doi: 10.1016/S0003-49160200018-0[2] Freedman M, Kitaev A, Larsen M, Wang Z 2003 Bull. Am. Math. Soc. 40 31 doi: 10.1090/S0273-0979-02-00964-3[3] Nayak C, Simon S H, Stern A, Freedman M, Sarma S D 2008 Rev. Mod. Phys. 80 1083 doi: 10.1103/RevModPhys.80.1083[4] Leinaas J M, Myrheim J 1977 Il Nuovo Cimento B 1971-1996 37 1 doi: 10.1007/BF02727953[5] Fredenhagen K, Rehren K H, Schroer B 1989 Commun. Math. Phys. 125 201 doi: 10.1007/BF01217906[6] Ivanov D A 2001 Phys. Rev. Lett. 86 268 doi: 10.1103/PhysRevLett.86.268[7] Read N, Green D 2000 Phys. Rev. B 61 10267 doi: 10.1103/PhysRevB.61.10267[8] Kitaev A Y 2001 Phys. Usp. 44 131 doi: 10.1070/1063-7869/44/10S/S29[9] Fu L, Kane C L 2008 Phys. Rev. Lett. 100 096407 doi: 10.1103/PhysRevLett.100.096407[10] Sato M, Takahashi Y, Fujimoto S 2009 Phys. Rev. Lett. 103 020401 doi: 10.1103/PhysRevLett.103.020401[11] Sau J D, Lutchyn R M, Tewari S, Sarma S D 2010 Phys. Rev. Lett. 104 040502 doi: 10.1103/PhysRevLett.104.040502[12] Lutchyn R M, Sau J D, Sarma S D 2010 Phys. Rev. Lett. 105 077001 doi: 10.1103/PhysRevLett.105.077001[13] Oreg Y, Refael G, von Oppen F 2010 Phys. Rev. Lett. 105 177002 doi: 10.1103/PhysRevLett.105.177002[14] Alicea J 2010 Phys. Rev. B 81 125318 doi: 10.1103/PhysRevB.81.125318[15] Alicea J 2012 Rep. Progress Physics 75 076501 doi: 10.1088/0034-4885/75/7/076501[16] Mourik V, Zuo K, Frolov S M, Plissard S R, Bakkers E P A M, Kouwenhoven L P 2012 Science 336 1003 doi: 10.1126/science.1222360[17] Deng M, Yu C, Huang G, Larsson M, Caroff P, Xu H 2012 Nano Lett. 12 6414 doi: 10.1021/nl303758w[18] Churchill H O H, Fatemi V, Grove-Rasmussen K, Deng M T, Caroff P, Xu H Q, Marcus C M 2013 Phys. Rev. B 87 241401 doi: 10.1103/PhysRevB.87.241401[19] Finck A D K, van Harlingen D J, Mohseni P K, Jung K, Li X 2013 Phys. Rev. Lett. 110 126406 doi: 10.1103/PhysRevLett.110.126406[20] Nadj-Perge S, Drozdov I K, Li J, Chen H, Jeon S, Seo J, MacDonald A H, Bernevig B A, Yazdani A 2014 Science 346 602 doi: 10.1126/science.1259327[21] Albrecht S M, Higginbotham A P, Madsen M, Kuemmeth F, Jespersen T S, Nygård J, Krogstrup P, Marcus C 2016 Nature 531 206 doi: 10.1038/nature17162[22] Deng M, Vaitiekėnas S, Hansen E B, Danon J, Leijnse M, Flensberg K, Nygård J, Krogstrup P, Marcus C M 2016 Science 354 1557 doi: 10.1126/science.aaf3961[23] Sun H H, Zhang K W, Hu L H, Li C, Wang G Y, Ma H Y, Xu Z A, Gao C L, Guan D D, Li Y Y, Liu C, Qian D, Zhou Y, Fu L, Li S C, Zhang F C, Jia J F 2016 Phys. Rev. Lett. 116 257003 doi: 10.1103/PhysRevLett.116.257003[24] Wang D F, Kong L Y, Fan P, et al. 2018 Science 362 333 doi: 10.1126/science.aao1797[25] Machida T, Sun Y, Pyon S, Takeda S, Kohsaka Y, Hanaguri T, Sasagawa T, Tamegai T 2019 Nat. Mater. 18 811 doi: 10.1038/s41563-019-0397-1[26] Liu Q, Chen C, Zhang T, Peng R, Yan Y J, Wen C H P, Lou X, Huang Y L, Tian J P, Dong X L, Wang G W, Bao W C, Wang Q H, Yin Z P, Zhao Z X, Feng D L 2018 Phys. Rev. X 8 041056 doi: 10.1103/PhysRevX.8.041056[27] Fornieri A, Whiticar A M, Setiawan F, et al. 2019 Nature 569 89 doi: 10.1038/s41586-019-1068-8[28] Ren H C, Pientka F, Hart S, et al. 2019 Nature 569 93 doi: 10.1038/s41586-019-1148-9[29] Chen C, Liu Q, Zhang T, Li D, Shen P, Dong X, Zhao Z X, Zhang T, Feng D 2019 Chin. Phys. Lett. 36 057403 doi: 10.1088/0256-307X/36/5/057403[30] Zhu S, Kong L, Cao L, et al. 2020 Science 367 189 doi: 10.1126/science.aax0274[31] Wang Z Y, Song H D, Pan D, Zhang Z T, Miao W T, Li R D, Cao Z, Zhang G, Liu L, Wen L J, Zhuo R, Liu D E, He K, Shang R, Zhao J, Zhang H 2022 Phys. Rev. Lett. 129 167702 doi: 10.1103/PhysRevLett.129.167702[32] Ménard G C, Anselmetti G L R, Martinez E A, Puglia D, Malinowski F K, Lee J S, Choi S, Pendharkar M, Palmstrøm C J, Flensberg K, Marcus C M, Casparis L, Higginbotham A P 2020 Phys. Rev. Lett. 124 036802 doi: 10.1103/PhysRevLett.124.036802[33] Puglia D, Martinez E A, Ménard G C, Pöschl A, Gronin S, Gardner G C, Kallaher R, Manfra M J, Marcus C M, Higginbotham A P, Casparis L 2021 Phys. Rev. B 103 235201 doi: 10.1103/PhysRevB.103.235201[34] Wang J Y, van Loo N, Mazur G P, Levajac V, Malinowski F K, Lemang M, Borsoi F, Badawy G, Gazibegovic S, Bakkers E P A M, Quintero-Pérez M, Heedt S, Kouwenhoven L P 2022 Phys. Rev. B 106 075306 doi: 10.1103/PhysRevB.106.075306[35] Aghaee M, Akkala A, Alam Z, et al. Microsoft Quantum 2023 Phys. Rev. B 107 245423 doi: 10.1103/PhysRevB.107.245423[36] Pöschl A, Danilenko A, Sabonis D, Kristjuhan K, Lindemann T, Thomas C, Manfra M J, Marcus C M 2022 Phys. Rev. B 106 L241301 doi: 10.1103/PhysRevB.106.L241301[37] Banerjee A, Lesser O, Rahman M A, Thomas C, Wang T, Manfra M J, Berg E, Oreg Y, Stern A, Marcus C M 2023 Phys. Rev. Lett. 130 096202 doi: 10.1103/PhysRevLett.130.096202[38] Zhang H, Liu D E, Wimmer M, Kouwenhoven L P 2019 Nat. Commun. 10 5128 doi: 10.1038/s41467-019-13133-1[39] Cao Z, Chen S, Zhang G, Liu D E 2023 Sci. China Phys. Mech. Astron. 66 267003 doi: 10.1007/s11433-022-1999-x[40] Hyart T, van Heck B, Fulga I C, Burrello M, Akhmerov A R, Beenakker C W J 2013 Phys. Rev. B 88 035121 doi: 10.1103/PhysRevB.88.035121[41] Aasen D, Hell M, Mishmash R V, Higginbotham A, Danon J, Leijnse M, Jespersen T S, Folk J A, Marcus C M, Flensberg K, Alicea J 2016 Phys. Rev. X 6 031016 doi: 10.1103/PhysRevX.6.031016[42] Clarke D J, Sau J D, Tewari S 2011 Phys. Rev. B 84 035120 doi: 10.1103/PhysRevB.84.035120[43] van Heck B, Akhmerov A, Hassler F, Burrello M, Beenakker C 2012 New J. Phys. 14 035019 doi: 10.1088/1367-2630/14/3/035019[44] Karzig T, Knapp C, Lutchyn R M, Bonderson P, Hastings M B, Nayak C, Alicea J, Flensberg K, Plugge S, Oreg Y, Marcus C M, Freedman M H 2017 Phys. Rev. B 95 235305 doi: 10.1103/PhysRevB.95.235305[45] Bell J S 1966 Rev. Mod. Phys. 38 447 doi: 10.1103/RevModPhys.38.447[46] Clauser J F, Horne M A, Shimony A, Holt R A 1969 Phys. Rev. Lett. 23 880 doi: 10.1103/PhysRevLett.23.880[47] de Lange G, van Heck B, Bruno A, van Woerkom D J, Geresdi A, Plissard S R, Bakkers E P A M, Akhmerov A R, DiCarlo L 2015 Phys. Rev. Lett. 115 127002 doi: 10.1103/PhysRevLett.115.127002[48] Larsen T W, Petersson K D, Kuemmeth F, Jespersen T S, Krogstrup P, Nygård J, Marcus C M 2015 Phys. Rev. Lett. 115 127001 doi: 10.1103/PhysRevLett.115.127001[49] Samkharadze N, Bruno A, Scarlino P, Zheng G, DiVincenzo D P, DiCarlo L, Vandersypen L M K 2016 Phys. Rev. Appl. 5 044004 doi: 10.1103/PhysRevApplied.5.044004[50] Hays M, de Lange G, Serniak K, van Woerkom D J, Bouman D, Krogstrup P, Nygård J, Geresdi A, Devoret M H 2018 Phys. Rev. Lett. 121 047001 doi: 10.1103/PhysRevLett.121.047001[51] Sabonis D, Erlandsson O, Kringhøj A, van Heck B, Larsen T W, Petkovic I, Krogstrup P, Petersson K D, Marcus C M 2020 Phys. Rev. Lett. 125 156804 doi: 10.1103/PhysRevLett.125.156804[52] Kroll J, Borsoi F, van der Enden K, Uilhoorn W, de Jong D, Quintero-Pérez M, van Woerkom D, Bruno A, Plissard S, Car D, Bakkers E, Cassidy M, Kouwenhoven L 2019 Phys. Rev. Appl. 11 064053 doi: 10.1103/PhysRevApplied.11.064053[53] Larsen T W, Gershenson M E, Casparis L, Kringhøj A, Pearson N J, McNeil R P G, Kuemmeth F, Krogstrup P, Petersson K D, Marcus C M 2020 Phys. Rev. Lett. 125 056801 doi: 10.1103/PhysRevLett.125.056801[54] van Zanten D M T, Sabonis D, Suter J, et al. 2020 Nat. Phys. 16 663 doi: 10.1038/s41567-020-0858-0[55] Bohm D 1952 Phys. Rev. 85 166 doi: 10.1103/PhysRev.85.166[56] Everett H 1957 Rev. Mod. Phys. 29 454 doi: 10.1103/RevModPhys.29.454[57] Aspect A, Dalibard J, Roger G 1982 Phys. Rev. Lett. 49 1804 doi: 10.1103/PhysRevLett.49.1804[58] Gisin N 1991 Phys. Lett. A 154 201 doi: 10.1016/0375-96019190805-I[59] Mermin N D 1993 Rev. Mod. Phys. 65 803 doi: 10.1103/RevModPhys.65.803[60] Bassi A, Ghirardi G 2003 Phys. Rep. 379 257 doi: 10.1016/S0370-15730300103-0[61] Aaronson S 2005 Phys. Rev. A 71 032325 doi: 10.1103/PhysRevA.71.032325[62] Genovese M 2005 Phys. Rep. 413 319 doi: 10.1016/j.physrep.2005.03.003[63] Leggett A J 2003 Found. Phys. 33 1469 doi: 10.1023/A:1026096313729[64] Spekkens R W 2007 Phys. Rev. A 75 032110 doi: 10.1103/PhysRevA.75.032110[65] Augusiak R, Demianowicz M, Acín A 2014 J. Phys. A 47 424002 doi: 10.1088/1751-8113/47/42/424002[66] Weihs G, Jennewein T, Simon C, Weinfurter H, Zeilinger A 1998 Phys. Rev. Lett. 81 5039 doi: 10.1103/PhysRevLett.81.5039[67] Simon C, Irvine W T M 2003 Phys. Rev. Lett. 91 110405 doi: 10.1103/PhysRevLett.91.110405[68] García-Patrón R, Fiurášek J, Cerf N J, Wenger J, Tualle-Brouri R, Grangier P 2004 Phys. Rev. Lett. 93 130409 doi: 10.1103/PhysRevLett.93.130409[69] Colbeck R, Renner R 2011 Nat. Commun. 2 1 doi: 10.1038/ncomms1416[70] Dada A C, Leach J, Buller G S, Padgett M J, Andersson E 2011 Nat. Phys. 7 677 doi: 10.1038/nphys1996[71] Hensen B, Bernien H, Dréau A E, et al. 2015 Nature 526 682 doi: 10.1038/nature15759[72] Hensen B, Kalb N, Blok M, et al. 2016 Sci. Reports 6 30289 doi: 10.1038/srep30289[73] Rosenfeld W, Burchardt D, Garthoff R, Redeker K, Ortegel N, Rau M, Weinfurter H 2017 Phys. Rev. Lett. 119 010402 doi: 10.1103/PhysRevLett.119.010402[74] Chtchelkatchev N M, Blatter G, Lesovik G B, Martin T 2002 Phys. Rev. B 66 161320 doi: 10.1103/PhysRevB.66.161320[75] Sauret O, Martin T, Feinberg D 2005 Phys. Rev. B 72 024544 doi: 10.1103/PhysRevB.72.024544[76] Zhong Y, Chang H S, Satzinger K, Chou M H, Bienfait A, Conner C, Dumur E, Grebel J, Peairs G, Povey R, et al. 2019 Nat. Phys. 15 741 doi: 10.1038/s41567-019-0507-7[77] Yao P, Hughes S 2009 Opt. Express 17 11505 doi: 10.1364/OE.17.011505[78] Pusey M F, Barrett J, Rudolph T 2012 Nat. Phys. 8 475 doi: 10.1038/nphys2309[79] Barrett J 2007 Phys. Rev. A 75 032304 doi: 10.1103/PhysRevA.75.032304[80] Leggett A J 2008 Rep. Prog. Phys. 71 022001 doi: 10.1088/0034-4885/71/2/022001[81] Harrigan N, Spekkens R W 2010 Found. Phys. 40 125 doi: 10.1007/s10701-009-9347-0[82] Barnum H, Barrett J, Clark L O, Leifer M, Spekkens R, Stepanik N, Wilce A, Wilke R 2010 New J. Phys. 12 033024 doi: 10.1088/1367-2630/12/3/033024[83] Fuchs C A, Schack R 2013 Rev. Mod. Phys. 85 1693 doi: 10.1103/RevModPhys.85.1693[84] Disilvestro L, Markham D 2017 Phys. Rev. A 95 052324 doi: 10.1103/PhysRevA.95.052324[85] See the Supplemental Information for more details.[86] Bravyi S, Kitaev A 2005 Phys. Rev. A 71 022316 doi: 10.1103/PhysRevA.71.022316[87] Deng D L, Duan L M 2013 Phys. Rev. A 88 012323 doi: 10.1103/PhysRevA.88.012323[88] Clarke D J, Sau J D, Sarma S D 2016 Phys. Rev. X 6 021005 doi: 10.1103/PhysRevX.6.021005[89] Romito A, Gefen Y 2017 Phys. Rev. Lett. 119 157702 doi: 10.1103/PhysRevLett.119.157702 -
Related Articles
[1] XUE Yu-Hao, HE Bing, ZHOU Jun, LI Zhen, FAN Yuan-Yuan, QI Yun-Feng, LIU Chi, YUAN Zhi-Jun, ZHANG Hai-Bo, LOU Qi-Hong. High Power Passive Phase Locking of Four Yb-Doped Fiber Amplifiers by an All-Optical Feedback Loop [J]. Chin. Phys. Lett., 2011, 28(5): 054212. doi: 10.1088/0256-307X/28/5/054212 [2] XU Shu-Wu, HUANG Yun-Xia, JI Xian-Ming. Field-Free Molecular Orientation Induced by Nonresonant Square Laser Pulses [J]. Chin. Phys. Lett., 2011, 28(4): 043301. doi: 10.1088/0256-307X/28/4/043301 [3] ZHOU Lei, NING Ji-Ping, CHEN Cheng, HAN Qun, ZHANG Wei-Yi, WANG Jun-Tao. High Power Er/Yb Codoped Double Clad Fiber Pulsed Amplifier Based on an All-Fiber Configuration [J]. Chin. Phys. Lett., 2009, 26(6): 064215. doi: 10.1088/0256-307X/26/6/064215 [4] HASI Wu-Li-Ji, FU Mei-Ling, LU Huan-Huan, GONG Sheng, LU Zhi-Wei, LIN Dian-Yang, HE Wei-Ming. Pulse Compression Based on Laser-Induced Optical Breakdown in Suspension [J]. Chin. Phys. Lett., 2009, 26(6): 064202. doi: 10.1088/0256-307X/26/6/064202 [5] Mehran Vahdani Moghaddam, Zeynab Chenari, Hamid Latifi, Vladimir Vladimirovich Shuvalov, Konestantin Valentinovich Rudenko. Numerical Simulation of Self-Pumped Phase Conjugate Plane--Curve Loop Mirror Based on Photorefractive Nonlinearity [J]. Chin. Phys. Lett., 2008, 25(8): 2888-2891. [6] SUI Zhan, LIN Hong-Huan, WANG Jian-Jun, ZHAO Hong-Ming, LI Ming-Zhong, QIAN Lie-Jia, ZHU He-Yuan, FAN Dian-Yuan. A Compact Nanosecond-Pulse Shaping System Based on Pulse Stacking in Fibres [J]. Chin. Phys. Lett., 2006, 23(8): 2074-2076. [7] CHI Rong-Hua, LU Ke-Cheng, YUN Peng, LI Yi-Gang, DONG Xiao-Yi, CHEN Wen-Zhao, YANG Guang-Ming, LIU Zhao-Bing. Performance Improvement of Distributed and Discrete Raman Amplifiers with a Fibre Loop Mirror [J]. Chin. Phys. Lett., 2003, 20(8): 1264-1268. [8] YANG Shi-Quan, ZHAO Chun-Liu, LI Zhao-Hui, YUAN Shu-Zhong, DONG Xiao-Yi. Optical Pulse Generation with Different Repetition Rates in aDual-Wavelength Actively Mode-Locked Fiber Ring Laser [J]. Chin. Phys. Lett., 2002, 19(6): 786-787. [9] CHEN Fei, HUO Yu-Jing, HE Shu-Fang, FENG Li-Chun. Diode-Pumped Nanosecond Pulsed Laser with Pulse-Transmission-Mode Q-Switch [J]. Chin. Phys. Lett., 2001, 18(2): 228-229. [10] TIAN Jian-Guo, WANG Hao-Hua, ZHOU Wen-Yuan, LI Tao, ZHANG Chun-Ping, ZHANG Guang-Yin. Analysis of the Influence of Thermal Effect on Z-Scan Measurements with a Nanosecond Pulse Laser [J]. Chin. Phys. Lett., 2000, 17(7): 510-512.
DownLoad: