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Chin. Phys. B, 2022, Vol. 31(6): 060301    DOI: 10.1088/1674-1056/ac5fa3
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Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

I Reena1, H S Karthik2, J Prabhu Tej3, Sudha4,5,†, A R Usha Devi1,5, and A K Rajagopal5
1 Department of Physics, Jnanabharathi, Bangalore University, Bangalore-560056, India;
2 International Centre for Theory of Quantum Technologies, University of Gdansk, Gdansk, 80-308, Poland;
3 Department of Physics, Ramaiah University of Applied Sciences, Bangalore-560054, India;
4 Department of Physics, Kuvempu University, Shankaraghatta, Shimoga-577 451, India;
5 Inspire Institute Inc., Alexandria, Virginia, 22303, USA
Abstract  We show that violation of the variance based local sum uncertainty relation (LSUR) for angular momentum operators of a bipartite system, proposed by Hofmann and Takeuchi [Phys. Rev. A 68 032103 (2003)], reflects entanglement in the equal bipartitions of an N-qubit symmetric state with even qubits. We establish the one-to-one connection with the violation of LSUR with negativity of covariance matrix [Phys. Lett. A 364 203 (2007)] of the two-qubit reduced system of a permutation symmetric N-qubit state.
Keywords:  sum uncertainty relations      permutation symmetry      rotational invariance  
Received:  18 August 2021      Revised:  15 December 2021      Accepted manuscript online:  22 March 2022
PACS:  03.65.Ud (Entanglement and quantum nonlocality)  
  03.67.-a (Quantum information)  
Fund: HSK acknowledges the support of NCN, SHENG (Grant No. 2018/30/Q/ST2/00625). IR, Sudha and ARU are supported by the Department of Science and Technology, India (Grant No. DST/ICPS/QUST/Theme-2/2019).
Corresponding Authors:  Sudha     E-mail:  arss@rediffmail.com

Cite this article: 

I Reena, H S Karthik, J Prabhu Tej, Sudha, A R Usha Devi, and A K Rajagopal Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems 2022 Chin. Phys. B 31 060301

[1] Heisenberg W 1927 Z. Phys. 43 172
[2] Kennard E H 1927 Z. Phys. 44 326
[3] Weyl H 1928 Gruppentheorie und Quantenmechanik (Leipzig: Hirzel)
[4] Robertson H P 1929 Phys. Rev. 34 163
[5] Bush P, Lahti P and Werner R F 2014 Rev. Mod. Phys. 86 1261
[6] Hofmann H F and Takeuchi S 2003 Phys. Rev. A 68 032103
[7] Hofmann H F 2003 Phys. Rev. A 68 034307
[8] Gühne O 2004 Phys. Rev. Lett. 92 117903
[9] Koashi M 2006 J. Phys.: Conf. Ser. 36 98
[10] Berta M, Christandl M, Colbeck R, Renes J M and Renner R 2010 Nat. Phys. 6 659
[11] Hänggi E and Renner R 2010 arXiv:1009.1833 [quant-ph]
[12] Tomamichel M and Renner R 2011 Phys. Rev. Lett. 106 110506
[13] Branciard C, Cavalcanti E G, Walborn S P, Scarani V and Wiseman H M 2012 Phys. Rev. A 85 010301
[14] Karthik H S, Usha Devi A R and Rajagopal A K 2015 Phys. Rev. A 91 012115
[15] Coles P J, Berta M, Tomamichel M and Wehner S 2017 Rev. Mod. Phys. 89 015002
[16] He Q Y, Shi-Guo Peng, Drummond P D and Reid M D 2011 Phys. Rev. A 84 022107
[17] Scully M O, Englert B G and Walther H 1991 Nature 351 111
[18] Pati A K and Sahu P K 2007 Phys. Lett. A 367 177
[19] Rivas A and Luis A 2008 Phys. Rev. A 77 022105
[20] Huang Y 2012 Phys. Rev. A 86 024101
[21] Maccone L and Pati A K 2014 Phys. Rev. Lett. 113 260401
[22] Chen B and Fei S M 2015 Sci. Rep. 5 14238
[23] Shabbir S and Björk G 2016 Phys. Rev. A 93 052101
[24] Xiao Y, Jing N, Li-Jost X and Fei S M 2016 Sci. Rep. 6 23201
[25] Bagchi S and Pati A K 2016 Phys. Rev. A 94 042104
[26] Ma W, Chen B, Liu Y, Wang M, Ye X, Kong F, Shi F, Fei S M and Du J 2017 Phys. Rev. Lett. 118 180402
[27] Song Q C, Li J L, Peng G X and Qiao C F 2017 Sci. Rep. 7 44764
[28] Hubert de Guise, Maccone L, Sanders B C and Shukla N 2018 Phys. Rev. A 98 042121
[29] Giorda P, Maccone L and Riccardi A 2019 Phys. Rev. A 99 052121
[30] Busch P and Reardon-Smith O 2019 arXiv:1901.03695 [quant-ph]
[31] Zheng X, Ma S and Zhang G 2020 Quantum Inf. Process. 19 116
[32] Szymański K and Życzkowski K 2020 J. Phys. A: Math. Theor. 53 015302
[33] Hirschman I I 1957 Am. J. Math. 79 152
[34] Beckner W 1975 Ann. Math. 102 159
[35] Bialynicki-Birula I and Mycielski J 1975 Commun. Math. Phys. 44 129
[36] Deutsch D 1983 Phys. Rev. Lett. 50 631
[37] Partovi M H 1983 Phys. Rev. Lett. 50 1883
[38] Bialynicki-Birula I 1984 Phys. Lett. A 103 253
[39] Kraus K 1987 Phys. Rev. D 35 3070
[40] Maassen H and Uffink J B M 1988 Phys. Rev. Lett. 60 1103
[41] Wehner S and Winter A 2010 New J. Phys. 12 025009
[42] Bialynicki-Birula I and Rudnicki L 2011 Statistical Complexity edited by Sen K (Dordrecht: Springer) p. 1
[43] Wang K, Zhan X, Bian Z, Li J, Zhang Y and Xue P 2016 Phys. Rev. A 93 052108
[44] Ma W, Chen B, Liu Y, Wang M, Ye X, Kong F, Shi F, Fei S M and Du J 2017 Phys. Rev. Lett. 118 180402
[45] Chen Z X, Li J L, Song Q C, Wang H, Zangi S M and Qiao C F 2017 Phys. Rev. A 96 062123
[46] Chen Z X, Wang H, Li J L, Song Q C and Qiao C F 2019 Sci. Rep. 9 5687
[47] Usha Devi A R, Uma M S, Prabhu R and Sudha 2006 Int. J. Mod. Phys. 20 1917
[48] Usha Devi A R, Uma M S, Prabhu R and Rajagopal A K 2007 Phys. Lett. A 364 203
[49] Usha Devi A R, Prabhu R and Rajagopal A K 2007 Phys. Rev. Lett. 98 060501
[50] Sorensen A, Duan L M, Cirac J I and Zoller P 2001 Nature 409 63
[51] Korbicz J K, Cirac J I and Lewenstein M 2005 Phys. Rev. Lett. 95 259901
[52] Usha Devi A R, Uma M S, Prabhu R and Sudha 2005 J. Opt. B 7 S740
[53] Korbicz J K, Gühne O, Lewenstein M, Häffner H, Roos C F and Blatt R 2006 Phys. Rev. A 74 052319
[54] Martin J, Giraud O, Braun P A, Braun D and Bastin T 2010 Phys. Rev. A 81 062347
[55] Markham D 2011 Phys. Rev. A 83 042332
[56] Usha Devi A R, Sudha and Rajagopal A K 2012 Quantum Inf. Proc. 11 685
[57] Lamata L, López C E, Lanyon B P, Bastin T, Retamal J C and Solano E 2013 Phys. Rev. A 87 032325
[58] Neven A, Martin J and Bastin T 2018 Phys. Rev. A 98 062335
[59] Srinivasa Rao K N 1988 Rotation and Lorentz Groups for Physicists (New York: John Wiley and Sons)
[60] Kitagawa M and Ueda M 1993 Phys. Rev. A 47 5138
[61] Akhilesh K S, Divyamani B G, Sudha, Usha Devi A R and Mallesh K S 2019 Quantum Inf. Proc. 18 144
[62] Wang X and Sanders B C 2003 Phys. Rev. A 68 012101
[63] Wang X and Molmer K 2002 Eur. Phys. J. D 18 385
[64] Usha Devi A R, Prabhu R and Rajagopal A K 2007 Phys. Rev. A 76 012322
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