# Nonlinear evolution and signaling

## TL;DR

This paper introduces a convex quasi-linearity condition for deterministic nonlinear quantum evolutions, ensuring they do not enable arbitrarily fast signaling, and provides an explicit example of such an evolution.

## Contribution

It proposes a new condition called convex quasi-linearity for nonlinear quantum evolutions and demonstrates its implications for signaling constraints.

## Key findings

- Nonlinear evolutions satisfying convex quasi-linearity do not permit arbitrary fast signaling.
- An explicit example of a nonlinear qubit evolution satisfying the quasi-linearity condition.
- The condition helps distinguish physically plausible nonlinear quantum evolutions.

## Abstract

We propose a condition, called convex quasi-linearity, for deterministic nonlinear quantum evolutions. Evolutions satisfying this condition do not allow for arbitrary fast signaling, therefore, they cannot be ruled out by a standard argument. We also give an explicit example of a nonlinear qubit evolution satisfying quasi-linearity.