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A model of correlated particles described by a generalized probability theoryis suggested whose dynamics is subject to a non-linear version of Schr\"odingerequation. Such equations arise in many different contexts, most notably in theproposals for the gravitationally induced collapse of wave function. Here, itis shown that the consequence of the connection demonstrates a possibledeviation of the theory from the standard formulation of quantum mechanics inthe probability prediction of experiments. The links are identified from thefact that the analytic solution of the equation is given by Dirichleteigenvalues which can be expressed by generalized trigonometric function.Consequently, modified formulation of Born's rule is obtained by relating theevent probability of the measuement to an arbitrary exponent of the modulus ofthe eigenvalue solution. Such system, which is subject to the non-lineardynamic equation, illustrates the violation of the Clauser-Hore-Shimony-Holtinequality proportional to the degree of the non-linearity as it can be testedby a real experiment. Depending upon the degree, it is found that the violationcan go beyond Tsirelson bound $2\sqrt{2}$ and reaches to the value of nonlocalbox.

Testable non-linearity through entanglement measurement