Experimental verification of the quantum nature of a neural network

Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual classical neural networks have some actual hidden quantum properties that make them such suitable tools for a highly coupled quantum problem. I discuss here what makes a system quantum and to what extent we can interpret a neural network as having quantum remnants. I suggest that a system can be quantum both due to its fundamental quantum constituents and due to the rules of its functioning, therefore, we can obtain entanglement both due to the quantum constituents' nature and due to the functioning rules, or, in category theory terms, both due to the quantum nature of the objects of a category and of the maps. From a practical point of view, I suggest a possible experiment that could extract entanglement from the quantum functioning rules (maps) of an otherwise classical (from the point of view of the constituents) neural network.