Effect of noise and enhancement of nonlocality in on/off photodetection
  Nonlocality of two-mode states of light is addressed by means of CHSH inequality based on displaced on/off photodetection. Effects due to non-unit 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 one 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 POVM, 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. 
Carmen Invernizzi, Stefano Olivares, Matteo G. A. Paris, Konrad   Banaszek