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Understanding non-classical correlation using optical hybrid states in noisy quantum channels

In this article we investigate the non-classical correlation in a macroscopic physical system. As a tool, we consider an optical hybrid state that is a micro–macro entangled state. Our strategy is to study the behavior of non-classical correlation in an optical hybrid state that may go through noisy channels. We study the violation of two inequalities, which are the CHSH-inequality and the (generalized) CHSH-like-inequality, as measures of non-classical correlation. First, we find that when on/off or parity measurements are used for the side of the coherent state in an optical hybrid state, the violation of the CHSH-inequality is the same as that of the (generalized) CHSH-like-inequality. Second, we see that each measurement provides a different value of violation of (generalized) CHSH-inequality when it is an optical hybrid state that goes through noisy channels. A suprising result is that the on/off measurement can provide a violation of CHSH-inequality (or (generalized) CHSH-like-inequality) for an optical hybrid state with any amount of colored noise. This implies that colored noise cannot break the non-classical correlation in an optical hybrid state.