We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that 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 the CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. It is also shown that two different classes of three-qubit pure symmetric states, consisting of two and three distinct constituent spinors (qubits) respectively, can be distinguished through the conditional CHSH non-locality test.We explore nonlocality of three-qubit pure symmetric states shared between Alice, Bob and Charlie using the Clauser-Horne-Shimony-Holt (CHSH) inequality. We show that 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 the CHSH test, after conditioning over measurement results of Charlie, nonlocality of the state is revealed. It is also shown that two different classes of three-qubit pure symmetric states, consisting of two and three distinct constituent spinors (qubits) respectively, can be distinguished through the conditional CHSH non-locality test.

May 6, 20200 citations

CHSH Violation for All Two-Qubit Measurement Settings

Daniel Dilley, Eric Chitambar

Bulletin of the American Physical SocietyMar 13, 20170 citations

Experimental test of CHSH inequality for non-maximally entangled states

Yun‐Feng Huang, Chuan‐Feng Li, Yong-Sheng Zhang +1 more

Physics Letters ASep 1, 20018 citations

CHSH inequality always holds in bipartite qutrits with spin-1 observables

Hyunho Cha, Jungwoo Lee

Bell inequalities reveal when quantum correlations cannot be explained by any local hidden-variable model, and the CHSH inequality is the most fundamental test of this phenomenon. While entangled two-qubit states can violate CHSH inequalities with suitable local measurements, the situation is more subtle for higher-dimensional systems when the allowed observables are physically restricted. In this work, we study bipartite qutrit systems in which each party is restricted to spin-1 observables $S(u)=u_xS_x+u_yS_y+u_zS_z$ , with $u\in\mathbb R^3$ a unit vector. Hanotel and Loubenets conjectured that nonseparable pure states of two qutrits do not violate the CHSH inequality under this measurement restriction. We prove the stronger result that every bipartite state on $\mathbb C^3\otimes\mathbb C^3$ , pure or mixed, satisfies the CHSH inequality for all choices of local spin-1 observables. Thus the absence of CHSH violation is not a property of special states, but a structural limitation of the spin-1 measurement family. Our result clarifies a distinction between two-qutrit entanglement and CHSH nonlocality under natural spin-component measurements.Bell inequalities reveal when quantum correlations cannot be explained by any local hidden-variable model, and the CHSH inequality is the most fundamental test of this phenomenon. While entangled two-qubit states can violate CHSH inequalities with suitable local measurements, the situation is more subtle for higher-dimensional systems when the allowed observables are physically restricted. In this work, we study bipartite qutrit systems in which each party is restricted to spin-1 observables $S(u)=u_xS_x+u_yS_y+u_zS_z$, with $u\in\mathbb R^3$ a unit vector. Hanotel and Loubenets conjectured that nonseparable pure states of two qutrits do not violate the CHSH inequality under this measurement restriction. We prove the stronger result that every bipartite state on $\mathbb C^3\otimes\mathbb C^3$, pure or mixed, satisfies the CHSH inequality for all choices of local spin-1 observables. Thus the absence of CHSH violation is not a property of special states, but a structural limitation of the spin-1 measurement family. Our result clarifies a distinction between two-qutrit entanglement and CHSH nonlocality under natural spin-component measurements.

quant-pharXiv:2603.10296Mar 12, 20260 citations

Trade-off relations of Bell violations among pairwise qubit systems

Huihui Qin, Shao-Ming Fei, Xianqing Li‐Jost

We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to illustrate the trade-off relations, and the trade-off relations are generalized to arbitrary multiqubit systems.We investigate the nonlocality distributions among multiqubit systems based on the maximal violations of the Clauser-Horne-Shimony-Holt (CHSH) inequality of reduced pairwise qubit systems. We present a trade-off relation satisfied by these maximal violations, which gives rise to restrictions on the distribution of nonlocality among the subqubit systems. For a three-qubit system, it is impossible that all pairs of qubits violate the CHSH inequality, and once a pair of qubits violates the CHSH inequality maximally, the other two pairs of qubits must both obey the CHSH inequality. Detailed examples are given to illustrate the trade-off relations, and the trade-off relations are generalized to arbitrary multiqubit systems.

arXiv:1512.08848Physical Review ADec 28, 201530 citations

S(u)=u_xS_x+u_yS_y+u_zS_z

, with

u\in\mathbb R^3

a unit vector. Hanotel and Loubenets conjectured that nonseparable pure states of two qutrits do not violate the CHSH inequality under this measurement restriction. We prove the stronger result that every bipartite state on

\mathbb C^3\otimes\mathbb C^3

, pure or mixed, satisfies the CHSH inequality for all choices of local spin-1 observables. Thus the absence of CHSH violation is not a property of special states, but a structural limitation of the spin-1 measurement family. Our result clarifies a distinction between two-qutrit entanglement and CHSH nonlocality under natural spin-component measurements.