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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

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