Testing quantum contextuality of continuous-variable states

We investigate the violation of non-contextuality by a class of continuous variable {states}, including variations of entangled coherent states (ECS) and a two-mode continuous superposition of coherent states. We generalise the Kochen-Specker (KS) inequality discussed in A. Cabello, Phys. Rev. Lett. 101, 210401 (2008) by using effective bidimensional observables implemented through physical operations acting on continuous variable states, in a way similar to an approach to the falsification of Bell-CHSH inequalities put forward recently. We test for state independent violation of KS inequalities under variable degrees of state entanglement and mixedness. We then demonstrate theoretically the violation of a KS inequality for any two-mode state by using pseudo-spin observables and a generalized quasi-probability function.