Tight nonclassicality criteria for unbalanced Hanbury Brown–Twiss measurement scheme with click detectors

We derive tight nonclassicality criteria for an unbalanced Hanbury Brown–Twiss measurement scheme, where an input optical beam is split into two outputs on an unbalanced beam splitter. The outputs are measured with binary click detectors, such as avalanche photodiodes, that can distinguish the presence and absence of photons. Our nonclassicality criteria have the form of tight lower and upper bounds on probability $p_{AB}$ of simultaneous no-clicks of both detectors for given probabilities $p_A$ and $p_B$ of no-clicks of the single detectors. These criteria are applicable to realistic detectors with limited detection efficiency. We show that the obtained criteria can detect nonclassicality of single-mode squeezed vacuum states.