Detecting entanglement in two-mode light states using generalized CHSH inequality

Entanglement can be detected between two modes of light by performing a Bell-type experiment involving Mach-Zehnder interferometers (MZIs) [1]. The experiment would involve a Mach-Zehnder interferometer, a strong coherent state and a photodetector forming a unit, each in two distant laboratories. Using two measurement settings per laboratory, controlled by the intensity of the coherent state, the maximal bound of such a CHSH inequality was verified to be $2sqrt{2}$. To improve the detection capabilities of the MZI-based CHSH inequality, we consider $n$ number of measurement settings of the interferometer in each lab and check for the maximum possible violations. We also make a comment on the maximal violations achieved by this generalized CHSH inequality for detecting entanglement in important classes of two-mode light states: entangled coherent states and two-mode squeezed vacuum, which are useful for quantum metrology [2].

[1] M. G. Dastidar, G. Sarbicki, Phys. Rev. A, 105, 062459. (2022)

[2] Polino et al, AVS Quantum Sci., 2(2), 024703. (2020)