  With the aid of a toy model, the Monty Hall Problem (MHP), the
counterintuitive and theoretically problematic concept of negative information
in classical systems is well understood. It is shown that, as its quantum
counterpart, classical local mutual information, obtained through a
measurement, can be expressed as the difference between the information gained
with the evidence and the negative information generated due to the
inefficiency of the measurement itself; a novel local Shannon metric, the
transfer information content, is defined as this difference, which is negative
if the measurement generates more disturbance than the evidence, i.e.,
generates a classical measurement back action. This metric is valid for both,
Classical and Quantum measurements, and it is proposed as a starting point
towards a general physical theory of information. This information-disturbance
trade-off in classical measurements is a kind of Heisenberg principle at
macroscopic scales, and it is proposed, as further work, to incorporate this
result in the already existing generalized uncertainty principles in the field
of quantum gravity.
