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. A68 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. A364 203 (2007)] of the two-qubit reduced system of a permutation symmetric N-qubit state.
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).
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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