I don't think this is an accurate summary of Marx's theories. Marx and Engels rejected the concept of the state employed by conservative and liberal political thinkers, contesting that the state was not a political formation existing above and beyond civil society, but something existing precisely within it, and so embodying certain aspects of that society. As such, the state follows rather than precedes the mode of production, so state ownership does not in itself indicate a socialist society. The state may simply be a grand, ultra-monopolistic capitalist enterprise.