We have some data on this from split-brain patients. These are people whose corpus callosum---a bundle of fibers linking their left and right cerebral hemispher

We have some data on this from split-brain patients. These are people whose corpus callosum---a bundle of fibers linking their left and right cerebral hemispheres---is cut. Such people start to act as if they are two individuals. Each hemisphere only has access to half of the visual field, and due to a quirk of how language is lateralized (typically left hemisphere only) they can make conflicting verbal and nonverbal reports of ambiguous stimuli: saying one thing yet writing another. So given this, it's not really fair to say that there is a unitary state to split. Each half would get a different state (perhaps "synchronized" at the time of the split), and only one half would be able to talk about the experience.