Is there truly classical information?

Abstract

All entropy is entanglement entropy. This appears as the result of the existence of black holes. The origin of entropy and the way in which it defines the perceived time direction in macroscopic systems has been discussed and can be debated as long as one ignores black holes. In such a case, thermodynamic entropy may define the arrow of time and entanglement entropy defines some special globally defined entropy encoding information in a non-local sense. With black holes however, if we accept that in-falling objects must have their information encoded outside, for example through non-local fluctuations away from thermalisation of the Hawking radiation, and that the horizon of a black hole cuts all classical information from the outside, then all the entropy that can be added to the black hole, which is basically any form of entropy, must be translated into some form of entanglement entropy to be detected outside. A discussion about the nature of information channels shows that spacetime may not be a correlation-insensitive channel as usually employed in the engineering of quantum computing. Time may emerge as a property of the complexity of entanglement spreading.