  Although the foundations of quantum and classical physics are much different,
it is often difficult to pinpoint which features of a particular system are
intrinsically "quantum". Perhapse, the most clear-cut distinction between
"classical" and "quantum" can be made for systems composed of many particles
when the properties of the ensemble are determined by the correlations between
the constituents. The issue of grasping the nature of entanglement (i.e.
quantum correlations) lies in its formal, discriminative definition: "if state
is not classical then it is entangled". A possible remedy would be to approach
the problem from the utilitarian point of view. The idea is that certain tasks
can be performed better when entangled states are used instead of states that
are only classically correlated. An example of such task is an
entanglement-enhanced interferometer utilizing ensembles of ultra-cold atoms.
This line of reasoning leads to the concept of classification of entanglement
by the degree of usefulness and allows to relate it to certain well-defined
physical properties of the state. The aim of this work is to formalize this
abstraction and build upon it an intuitive picture which can help us understand
what the entanglement is.
