Testable non-linearity through entanglement measurement

TL;DR

This paper proposes a non-linear extension of quantum mechanics based on entanglement measurement, predicting deviations from standard quantum theory and potential violations of Bell inequalities beyond Tsirelson's bound, testable in experiments.

Contribution

It introduces a non-linear Schrödinger equation model linked to generalized probability theory, predicting observable deviations from standard quantum mechanics.

Findings

Violates Bell inequalities proportionally to non-linearity degree

Can exceed Tsirelson's bound up to nonlocal box limit

Provides a modified Born's rule based on eigenvalue solutions

Abstract

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 $2\sqrt{2}$ and reaches to the value of nonlocal box.