Algebry operatorów i ich zastosowania w fizyce

I will discuss the general aspects of testing the postulates of local realism with massive particles. It will be shown that for such objects not only the mode- but also the particle entanglement is a necessary resource to run any Bell-like test. Next, I will propose an experiment, where the Bell inequality is violated in a many-body system of massive particles. The source of correlated atoms is a spinor F = 1 Bose-Einstein condensate residing in an optical lattice. I will characterize the complete experimental procedure— the local operations, the measurements and the inequality—necessary to run the Bell test. I will show that the system can be used to demonstrate the Einstein-Podolsky-Rosen paradox. Also, the scattered pairs are an excellent many-body resource for the quantum-enhanced metrology.