Non-Classicality Indicators of Entangled and Squeezed Number States

Many non-classicality indicators are used to measure the quantum effects of different systems. Kenfack's and Sadeghi's non-classicality indicators are introduced regarding the amount of Wigner distribution function's negativities and interferences in phase space quantum mechanics, respectively. Kenfack’s non-classicality indicator is used for cases just in the Wigner representation, whereas Sadeghi’s non-classicality indicator is effectively, applied for some real distribution functions. In this paper, we investigate these non-classicality indicators for the entangled photon number states in the Wigner, Husimi, and Rivier representations. It is shown that for a two-level entangled state, Sadeghi's indicator has more benefits to measure entanglement with respect to Kenfack's indicator. For the two-level entangled state, we also show a correspondence between Sadeghi's non-classicality indicator and the Von Neumann entropy. It is also shown that for the superposition of the squeezed number state and ground number state, the squeezing parameter affects the entanglement feature and Sadeghi's non-classicality indicator increases with the increase of the squeezing parameter.