Way back in 1781 Immanuel Kant discussed this (without considering quantum implications, obviously) in "Critique of Pure Reason". He coined the term "noumenon" to describe a thing as it is, not as it is perceived.
For a while now, I’ve been intrigued by the possibility of literally unthinkable thoughts; something that is outside the capacity of human neural architecture in the way that HTML is outside [0] the capacity of RegEx?
1. It could be uncomputable, since it seems likely to me that we can't think uncomputable thoughts. (Not a rigorous scientific hypothesis, but it seems more likely than not to me.)
2. It could be uncomputable in a human lifetime. I think these already exist today: can anyone really be said to thoroughly understand a proof generated by an exhaustive computational search?
One can play around with the semantics of what we mean by "unthinkable" and "thought," but I think "computable" at least provides one interesting start to an exploration of this concept.
Can an octopus mind, for a body with eight limbs but no bones, ever be accurately emulated by a human mind?
Are there truths we can only reach with an exocortex (pen and paper included)?
Are there thoughts whose time or space requirements grow exponentially with respect to some measure in a human brain anatomy, but which could be linear in some other anatomy (existing or hypothetical)?
A simple example: in his boo The Crystal and the Way of Light, Namkhai Norbu describes one of his meditational experiences where he sees 5 spheres of light in one bigger sphere. In this experience, there is no space between the spheres but this seemed perfectly natural. After he finished the practice session, he sat and tried to draw it and after several attempts realized it's impossible. There are many similar accounts.
(Kantian noumena) of human perception and are not ontologically exhausted by their relations with humans or other objects. The article, as it appears, all relations, including those between nonhumans, distort their related objects in the same basic manner as human consciousness and exist on an equal footing with one another.