Testing quantum correlations with generalized quasi-probabilities under uncontrollable noises

We introduce a method for testing quantum correlations in terms of generalized quasi-probability distributions when uncontrollable noises are involved in the measuring devices as well as in the system prepared. The order parameter of the generalized quasi-probability functions provides distributed matching values to the photon number statistics, as it modifies the bosonic operator ordering. Our formalism provides a noise adaptive quasi-probability function by a disproportional assignment of the values to the photon number distribution under the effect of noises. Remarkably, using the formalism, it is possible to observe quantum correlations of continuous variable systems in the presence of severe uncontrollable noises. Our scheme provides a useful tool to test quantum correlations in various protocols with near-term noisy quantum information processors with continuous variable systems.