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A sequence of weakly measured moments of an observable can be associated to a conditional quasidistribution. The Based on the probabilistic behavior of this quasidistribution, recently, we introduced a new definition of  nonclassicality of the system state in the sense of weak measurements. In this paper, using this definition, we examine witnesses of nonclassicality of the thermal states in weak measurement of momentum . To this end, we consider weak measurement of momentum  conditioned on the outcome of strong measurement of position  on the target system. We calculate weak values of quasi-moments of the momentum in the thermal states. Then, we plot the witnesses of nonclassicality as a function of q for these states. Using numerical results, we obtain points that thermal states behave nonclassical in these points. Also, we find conditional quasidistribution in weak measurements in terms of the Glauber quasidistribution and Wigner quasidistribution of the state. Then, we present the differences between nonclassicality based on Glauber's definition and nonclassicality in weak measurements. Using the Glauber distribution of the thermal states, we calculate conditional quasidistribution related of the moments of momentum  and show why classical states behave nonclassical in weak measurements.

Keywords: quasidistribution, nonclassicality, weak measurements, weak values, Glauber quasi-distribution

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