Bell’s Inequality for a Particle

Shahpoor Moradi

For two particles with different spin, we derive the Bell's inequality. The inequality is investigated for two systems combining spin-1 and 1/2; spin-1/2 and 3/2. We show that for these states Bell's inequality is violated.

M. Revzen, A. Mann

D. Gutkowski, G. Masotto

Fabian Bernards, Otfried Gühne

Bell inequalities are relevant for many problems in quantum information science, but finding them for many particles is computationally hard. Recently, a computationally feasible method called cone-projection technique has been developed to find all optimal Bell inequalities under some constraints, which may be given by some symmetry or other linear conditions. In this paper we extend this work in several directions. We use the method to generalize the I4422 inequality to three particles and a so-called guess-your-neighbor's-input inequality to four particles. Additionally, we find Bell inequalities for three particles that generalize the I3322 inequality and the Clauser-Horne-Shimony-Holt inequality at the same time. We discuss the obtained inequalities in some detail and characterize their violation in quantum mechanics.

Daniel L. Schauer

Jing‐Ling Chen, Chunfeng Wu, L. C. Kwek +1 more

In the work, we present the structure of the tight Bell inequalities for three-particle systems. Interesting Bell inequalities for three qubits that reducing from those of three qudits are also studied.