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Testable non-linearity through entanglement measurement
A model of correlated particles described by a generalized probability theory
is suggested whose dynamics is subject to a non-linear version of Schr\"odinger
equation. Such equations arise in many different contexts, most notably in the
proposals for the gravitationally induced collapse of wave function. Here, it
is shown that the consequence of the connection demonstrates a possible
deviation of the theory from the standard formulation of quantum mechanics in
the probability prediction of experiments. The links are identified from the
fact that the analytic solution of the equation is given by Dirichlet
eigenvalues which can be expressed by generalized trigonometric function.
Consequently, modified formulation of Born's rule is obtained by relating the
event probability of the measuement to an arbitrary exponent of the modulus of
the eigenvalue solution. Such system, which is subject to the non-linear
dynamic equation, illustrates the violation of the Clauser-Hore-Shimony-Holt
inequality proportional to the degree of the non-linearity as it can be tested
by a real experiment. Depending upon the degree, it is found that the violation
can go beyond Tsirelson bound and reaches to the value of nonlocal
box.Comment: 3 figure
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