  The work is organized in two main topics. At first we will outline the
relation between spin squeezing, quantum metrology and entanglement detection,
with a particular focus on the last. We will derive spin squeezing criteria for
the detection of entanglement and its depth that outperform past approaches,
especially for unpolarized states, recently produced in experiments and object
of increasing interest in the community. Furthermore, we will extend the
original definition of spin squeezed states by providing a new parameter that
is thought to embrace different classes of states in a unified framework.
  Afterwards we consider a test of quantum principles in macroscopic objects
originally designed by Leggett and Garg. In this case the scenario consists of
a single party that is probed at different time instants and the quantum effect
detected is the violation of Macrorealism (MR), due to strong correlations in
time, rather than in space, between non-compatible observables. We will look at
the problems of inconclusiveness of the LG tests arising from possible
explanations of the results in terms of ``clumsy'' measurements, what has been
termed ``clumsiness loophole''.
  We propose first a scheme to test and possibly falsify (MR) in macroscopic
ensembles of cold atoms based on alternating Quantum Non-Demolition
measurements and coherent, magnetically-driven collective spin rotations. Then
we also propose a way to address the clumsiness loophole by introducing and
computing an invasivity quantifier to add to the original LG expression. We
provide numerical evidence that such a clumsiness-free test is feasible under
state-of-the-art realistic experimental parameters and imperfections.
