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

We show, by explicit examples, that the Jaynes principle when applied to co mpound quantum systems may produce the entangled maximum entropy states com patible with data coming from nonentangled (separable) states. It means tha t the Jaynes statistical inference scheme may lead to a wrong conclusion ab out entanglement, which is a crucial parameter in quantum information theor y. We suggest that in all the processes where entanglement is needed, the p roper inference scheme should involve minimization of entanglement. Example s illustrating the proposed scheme are provided. [S1050-2947(99)02303-3].