Information is the state of a system of interest. Message is the information materialized.

Information is a quality of a message from a sender to one or more receivers. Information is always about something (size of a parameter, occurrence of an event, etc).

http://mathcenter-k6.haifa.ac.il/mispar_chazak/11/hu...

Quantum probability rule: If M is a quantum measurement and
E belongs to E_M, then the probability of E given that M is performed is
equal to W_M(E).

Familiar though it may be, do we actually understand it? Compare it with
the

Quantum sqwerdleflunkicity rule: If M is a quantum measurement
and E belongs to EM, then the sqwerdleflunkicity of E given that M is
performed is equal to W_M(E).

We don’t understand the quantum sqwerdleflunkicity rule, and for an obvious
reason: “sqwerdleflunkicity” is meaningless, or at any rate we have no idea what
it is supposed to mean. So if we do understand the quantum probability rule,
presumably this requires that we understand what “probability” means.
But in fact, the meaning of “probability” is pretty subtle, and pretty controversial.

In principle, we might go further. An agent judges E and F to be equally
likely iff he is indifferent between a bet on E and one on F; if he judges disjoint
events E and F to be equally likely, and judges G to be equally likely as E [F,
then we say that he judges G to be twice as likely as E