Quantum mechanics is a linear theory. This property is so fundamental that violating it would mean losing the superposition principle and, consequently, the possibility of superluminal information transfer. But physicists have long suspected that at a deep level, where gravity meets quanta, linearity might not survive. Einstein's equations are nonlinear, and if quantum gravity exists, it may inherit that nonlinearity. Three well-known models: the Deutsch map, the Weinberg model, and the Schrödinger–Newton equation, offer concrete ways to "bend" quantum mechanics. The question is how to distinguish them from standard theory in the lab.

Nonlinearity erases quantum correlations like an eraser removes pencil marks. Contextuality is a property of quantum systems where the outcome of a measurement depends on what other quantities are measured simultaneously. Imagine four qubit states lying on the same meridian of the Bloch sphere. Their density matrices are linearly dependent, and this set is contextual: no classical hidden-variable model can reproduce the measurement statistics. The authors prove a theorem: a set of pure states is noncontextual if and only if their density matrices are linearly independent. This is a simple algebraic criterion that turns a complex quantum effect into a rank check.

Applying this criterion to the three nonlinear models, the authors found a common pattern. In the Weinberg model, four states on the same meridian of the Bloch sphere, after nonlinear evolution, end up on different meridians, and their density matrices become linearly independent. In the Schrödinger–Newton equation, which describes the gravitational self-interaction of the wave function, the effect appears already in the first order of iterations: a phase shift that depends on the wave function separates the states. The Deutsch map, based on closed timelike curves, behaves similarly. Nonlinearity acts like an eraser: it wipes out delicate quantum correlations, making the system classically explainable.

This opens the way to experimental tests of nonlinear modifications of quantum mechanics without using entangled states. It suffices to prepare a single qubit in one of four states, measure the violation of a noncontextuality inequality, then subject the system to nonlinear evolution and measure again. If the violation disappears, the nonlinear model survives; if not, it is rejected. Such a test is analogous to checking Bell inequalities, but it works on a single quantum system and avoids signaling problems. The immediate next step is to generalize the criterion to continuous variables, to reach atomic interferometry, where the Schrödinger–Newton equation manifests itself most clearly. Perhaps this is how we will learn whether quantum mechanics is truly linear at the deepest levels of reality.