  The thesis is divided into three parts. In the first part a new theoretical
analysis of interferometric experiments by Alley-Shih, Ou-Mandel and the
entanglement swapping experiment is performed. It is shown that the double- and
single-photon distinguishability is not necessary for the experiments to be
genuine tests against local realism. In the second part, basing on simple
geometrical properties of Hilbert space, new, stronger Bell inequalities for M
qubits in a maximally entangled state are derived. Application of the same
method to two maximally entangled qubits yields an inequality for all possible
positions of the local measuring apparatus. Finally, the series of the
Greenberger-Horne- Zeilinger paradoxes for M maximally entangled quNits
observed via symmetric unbiased 2N ports is derived. The last part of the
thesis is devoted to the numerical approach to the Bell theorem. The necessary
and sufficient conditions for the violation of local realism in the case of two
and three maximally entangled qubits, on which each observer performs up to 10
(two qubits) and up to 5 (three qubits) local measurements, are shown. It is
also numerically shown that in the case of two maximally entangled quNits (3 <
N < 9) a properly defined magnitude of violation increases with N. In both
cases the approach neither involves any simplifications, or additional
assumptions, nor does it utilise any symmetries of the problem.
