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We investigate the violation of Leggett's inequality for non-local realismusing entangled coherent states and various types of local measurements. Weprove mathematically the relation between the violation of theClauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one whentested by the same resources. For Leggett inequalities, we generalize thenon-local realistic bound to systems in Hilbert spaces larger thanbidimensional ones and introduce an optimization technique that allows toachieve larger degrees of violation by adjusting the local measurementsettings. Our work describes the steps that should be performed to produce aself-consistent generalization of Leggett's original arguments tocontinuous-variable states.

Faithful test of non-local realism with entangled coherent states