Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

doi:10.1088/1674-1056/ac5fa3

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/ac5fa3

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

I Reena¹, H S Karthik², J Prabhu Tej³, Sudha^4,5,†, A R Usha Devi^1,5, 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

收稿日期:2021-08-18 修回日期:2021-12-15 接受日期:2022-03-22 出版日期:2022-05-17 发布日期:2022-05-17
通讯作者: Sudha E-mail:arss@rediffmail.com
基金资助:
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).

Local sum uncertainty relations for angular momentum operators of bipartite permutation symmetric systems

I Reena¹, H S Karthik², J Prabhu Tej³, Sudha^4,5,†, A R Usha Devi^1,5, 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

Received:2021-08-18 Revised:2021-12-15 Accepted:2022-03-22 Online:2022-05-17 Published:2022-05-17
Contact: Sudha E-mail:arss@rediffmail.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: sum uncertainty relations, permutation symmetry, rotational invariance

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.

Key words: sum uncertainty relations, permutation symmetry, rotational invariance

中图分类号: (Entanglement and quantum nonlocality)

03.65.Ud

03.67.-a (Quantum information)

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[J]. 中国物理B, 2022, 31(6): 60301-060301.

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