A new Bell inequality for three spin-half particle system

Xiaohua Wu, Hong-Shi Zong, Pang Hou-Rong +1 more

Shahpoor, Moradi

Brian J. Oliver, Carlos R. Stroud

The analogy between two-level atoms and spins is used to show that Rydberg atoms provide a new medium through which Bell’s inequalities may be studied. The low-efficiency particle detectors that have been used in experiments to test Bell’s inequalities are replaced by nearly 100% efficient state-selective ionizers in Rydberg-atom experiments. Two methods for producing correlated states of pairs of atoms are discussed. Each method can be used to create correlated states of more than two atoms. A Bell inequality for a three-atom system is considered and compared with quantum-mechanical predictions. A violation of the inequality for the three-particle system is predicted.

V. A. Andreev, Vladimir I. Man’ko

Jiaqiang Zhao, Meijiao Wang, Lianzhen Cao +5 more

Knowing the level of entanglement robustness against quantum bit loss or decoherence mechanisms is an important issue for any application of quantum information. Fidelity of states can be used to judge whether there is entanglement in multi-particle systems. It is well known that quantum channel security in QKD can be estimated by measuring the robustness of Bell-type inequality against noise. We experimentally investigate a new Bell-type inequality (NBTI) in the three-photon Greenberger-Horne-Zeilinger (GHZ) states with different levels of spin-flip noise. The results show that the fidelity and the degree of violation of the NBTI decrease monotonically with the increase of noise intensity. They also provide a method to judge whether there is entanglement in three-particle mixed states.

V. M. González-Robles

John Ju Sakurai's classical book in quantum mechanics makes a very illuminative presentation that studies entangled states in a two spin s=1/2 particles system in a singlet state. A Bell's inequality emerges as a consequence. Bell's inequality is a relationship among observables that discriminates between Einstein's locality principle and the nonlocal point of view of orthodox quantum mechanics. Following Sakurai's style we propose, by making natural induction, a generalization for Bell's inequality for any two spin-s particles in a singlet state (s integer or half-integer). This inequality is expressed as a function of a θ parameter, which is a measure of the angle between two possible directions in which the spin is measured. Besides the expression for this general inequality we have found that: (a) for any finite half-integer spin Bell's inequality is violated for some interval of the θ-parameter. The right limit of this interval is fixed and equal to π/2, while the left one comes closer and closer to this value as spin number grows. A function fit shows clearly that the size of this θ-interval over which Bell's inequality is violated diminishes asymptotically to zero as 1/s1/2; (b) an analogous behavior for any finite integer spin. For large spins the disagreement between Einstein's locality principle and the nonlocal point of view in orthodox quantum mechanics disappears.