Nonlinear quantum mechanics allows better cloning without signalling

We present a nonlinear generalization of quantum mechanics where one can copy arbitrary pure states with fidelities higher than those of the quantum cloners. Weinberg's nonlinear quantum mechanics has been criticized for its possible implications for superluminal communication. We demonstrate that universal symmetric cloners can make better copies than standard quantum ones and yet they do not violate the no-signalling principle. If linearity constraint is added, we show that for a given fidelity there is a unique cloner which can be written down explicitly. [1] Z. Gedik, B. Cakmak, arXiv:1203.3054v2 (2012).