See the following articles:
Recently a number of articles, like those above, have appeared which express the opinion of two prominent physical scientists that claim to have proved the existence of a soul which survives our physical death. They define the soul as information and show that quantum entanglement demonstrates that information carried by a particle can remain accessible even after its extinction.
The phenomenon of Quantum Entanglement is used as evidence of the existence of information carried by a particle, entangled with another, even after the particle is absorbed. For the sake of argument, I will assume that the interpretation placed on such experiments is correct, that in fact information carried by physical matter is preserved even after that matter is converted to energy and so could be loosely said to be annihilated.
This of course says nothing much about consciousness and its survival after physical death, but it does provide support for a possible connection of such a subjective hypothesis to objective science.
I myself find the argument that our consciousness cannot be a property of physical matter convincing of the non-material nature of consciousness and therefore our soul. I believe that I can prove that statement by proving that there is no possibility of an objective way to detect the existence of consciousness.
I maintain that all physical properties, including any emergent physical properties, must necessarily be physically, objectively detectable. Some have argued against that proposition, saying that emergent properties need only be subjectively detectable. However that definition essentially defines, with no justification, all subjectivity and all subjective experiences, which are based on our consciousness and include consciousness, as emergent properties. If that definition is accepted, then emergent properties can include non-physical properties and no one can possibly prove objectively that non-physical properties, however they are brought about, arise out of matter.
All the science which studies our brains and their function and relates it to our subjective experiences only shows correlates of brain action to subjective experiences. Correlation is no proof of causation and therefore no current observations show any causation of consciousness, that is we have no idea what causes consciousness. It is impossible and will always remain impossible to prove objectively that any particular physical phenomena are the causes of consciousness. The justifications of this statement are in my Kindle book.