Effect of noise and enhancement of nonlocality in on/off photodetection

Nonlocality of two-mode states of light is addressed by means of Clauser-Horne-Shimony-Holt (CHSH) inequality based on displaced on/off photodetection. Effects due to nonunit quantum efficiency and nonzero dark counts are taken into account. Nonlocality of both balanced and unbalanced superpositions of few photon-number states, as well as that of multiphoton twin beams, is investigated. We find that unbalanced superpositions show larger nonlocality than balanced ones when noise affects the photodetection process. De-Gaussification by means of (inconclusive) photon subtraction is shown to enhance nonlocality of twin beams in the low-energy regime. We also show that when the measurement is described by a positive operator-valued measure, rather than a set of projectors, the maximum achievable value of the Bell parameter in the CHSH inequality is decreased, and is no longer given by the Cirel’son bound.