Characterizing nonlocality of pure symmetric three-qubit states

We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We make use of the elegant parametrization in the canonical form of these states, proposed by Meill and Meyer (Phys. Rev. A 96, 062310 (2017)) based on Majorana geometric representation. The reduced two-qubit states, extracted from an arbitrary pure entangled symmetric three-qubit state do not violate the CHSH inequality and hence they are CHSH-local . However, when Alice and Bob perform a CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. We have also shown that two different families of three-qubit pure symmetric states, consisting Corresponding author: Sudha K. Anjali Department of Physics, Bangalore University, Bangalore-560 056, India Akshata Shenoy Hejamadi International Centre for Theory of Quantum Technologies, University of Gdansk, Gdansk, Poland H. S. Karthik International Centre for Theory of Quantum Technologies, University of Gdansk, Gdansk, Poland S. Sahu School of Electronics and Electrical Engineering, University of Leeds, Leeds, UK Sudha Department of Physics, Kuvempu University, Shankaraghatta-577 451, India E-mail: arss@rediffmail.com Inspire Institute Inc., Alexandria, Virginia, 22303, USA. A. R. Usha Devi Department of Physics, Bangalore University, Bangalore-560 056, India Inspire Institute Inc., Alexandria, Virginia, 22303, USA. ar X iv :2 00 5. 02 94 3v 4 [ qu an tph ] 3 N ov 2 02 1