a simple test about potential uniatrity violations in the black hole firewall paradox
We propose a simple test designed to detect non unitary effects in the black hole evaporation. Since the effects are expected to be tiny, the test relies on information theory in order to discriminate between the non unitary hypothesis and the unitary hypothesis. We show that the modification of the (final) mass of an isolated black hole would imply a modification in the non-unitary effects within its evaporation. Thus the effect should affect any quantum measure standing on the causal past of any mass absorption event. However shooting a mass toward a black hole in our galaxy would not lead to a detectable non unitary effect since most of the matter in the galaxy would eventually end in the central black hole. Therefore the test is based on expelling flows of particles outward the galaxy. Before any mass expulsion, one creates a binary codeword from a sequence of spin measurements, and performs a protocol of mass expulsion based on the codeword. Given a fixed quantity of mass to be expelled, the protocol would maximize the likelihood of the discrimination between unitary and non unitary effect via the Kullback-Leibler divergence. In term of information theory, this is equivalent to consider the extraction of one bit of information from a received codeword, the bit corresponds to the a posteriori application of a protocol with mass expulsion versus the alternative protocol without mass expulsion. Assuming accumulation in non unitary effects, this channel has a larger capacity than classic symmetric channels.