The quantum nature of consciousness

The following quote appears in the book Consciousness by Susan Blackmore:

According to Dennet the brain processes multiple parallel descriptions of the world all the time, and none of them is either 'in' or 'out' of consciousness. When the system is probed in a certain way—say by asking someone to answer a question or respond to a stimulus—he may decide what he is conscious of and tell you about it. But up to that point there was no truth of the matter about whether that thing was, or was not, 'in consciousness'.

It's hard not to think about quantum physics when reading such a statement. Could consciousness be somewhat quantum-mechanical?

From Wikipedia:

The quantum mind or quantum consciousness is a group of hypotheses proposing that classical mechanics cannot explain consciousness. It posits that quantum-mechanical phenomena, such as entanglement and superposition, may play an important part in the brain's function and could explain consciousness.

However, this idea is still in the realm of philosophy, and considered pseudoscience by some. Even Daniel Dennett himself does not believe that quantum effects are needed to explain consciousness (to be verified).