Testing Bell inequalities for multi-partite systems with frequency-encoded photonic qubits

Generalizing the problem of state nonlocality measurement, we suggest a multi-partite Bell test for multi-photon frequency-entangled quantum state in a quantum network. Each side of this network is equipped with a generalized detector, consisting of an electro-optic phase modulator, frequency filter and photo-counter. In our paper, we develop a theory of Bell nonlocality measurement in frequency domain, using generalized Svetlichny inequalities. Solving the optimization problem for detectors inputs, we obtain optimal measurement parameters which allow strong violation of considered inequalities. As a particular case, we consider bi- and tripartite cases for EPR, GHZ and Wigner states correspondingly.