Entanglement processing and statistical inference: The Jaynes principle can produce fake entanglement

We show, by explicit examples, that the Jaynes principle when applied to compound quantum systems may produce the entangled maximum entropy states compatible with data coming from nonentangled (separable) states. It means that the Jaynes statistical inference scheme may lead to a wrong conclusion about entanglement, which is a crucial parameter in quantum information theory. We suggest that in all the processes where entanglement is needed, the proper inference scheme should involve minimization of entanglement. Examples illustrating the proposed scheme are provided.