Dual problem of nonclassicality

We show that nonclassicality of phase-space quasi-probability distributions is tied to violations of principles of physical reality in device-dependent scenarios. In this context, the nonclassicality problem has its dual form expressed as a device-dependent analog of Bell inequalities. This approach is applicable even to systems with only one spatial party. The derived inequalities are employed for testing nonclassicality with emblematic optical measurements: photocounting including the case of realistic photon-number resolution; unbalanced, balanced, and eight-port homodyne detection.