Classical limit of entangled states

Speaker: Prof. Marek Kuś
Affiliation: Center for Theoretical Physics, Warsaw

A large quantum system should exhibit classical features. This is the main idea of the correspondence principle formulated by Bohr in the first years of quantum mechanics. There still is a question how this classical behavior is reached. This applies in particular to systems in entangled states. A quantum system in an entangled state consists of two subsystems, and coherence between these subsystems is the essence of entanglement. Entanglement can be tested using Bell’s inequality, broken by entangled states.   On the other hand, classical systems do not manifest correlations related to entanglement. So what happens to entanglement in the classical limit?
To illuminate some aspects of this problem I consider a system of two particles, each with large angular momentum, in the singlet state. The generalized Bell inequalities are formulated in terms of the probabilities of finding projections of the angular momenta on selected axes. I show that most of Bell’s inequalities cannot be violated, or are violated only marginally, in the classical limit of large angular momenta. The precision required to confirm a violation appears to be difficult to achieve. In practice, the quantum system, in spite of being entangled, becomes indistinguishable from its classical counterpart.

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