Violation of Bell-type Inequality in the Hanbury Brown-Twiss (HBT) Toy-Model: Quantum Correlations beyond Local-Realism

The Hanbury Brown-Twiss (HBT) effect marked a significant milestone in quantum optics by illustrating that intensity correlations can reveal inherently quantum features of light. Motivated by the structure of the original 8-mode HBT interferometer, we develop a simplified 4-mode toy-model that captures its essential physical ingredients while significantly reducing analytical complexity. Our toy-model provides an intuitive and well-structured framework for examining the desired correlation functions. We investigate whether our toy-model can exhibit genuinely non-classical behaviour by formulating and applying a Bell-type inequality tailored to its specific measurement configuration. Our analysis shows that the correlations generated by the toy-model violate the inequality, indicating the presence of non-local features that are incompatible with any classical hidden-variable description. The results highlight the power of simplified models in uncovering fundamental aspects of non-classicality in optical systems.