### Abstract

There are two ways of doing quantum information theory beyond qubits. One task is to investigate its basic notions in the new situations. The familiar entities there acquire some unusual properties. Entropy is observer-dependent, but not always so. Entanglement measures may be observer-dependent as well. We discuss the reasons for this dependence and the implications of both invariance and non-invariance, illustrating by the geometric entropy in quantum field theory and black hole entropy.

On the other hand, we may apply quantum information to the problems in other areas. For example, the logarithmic corrections for the black hole entropy may be related to the entanglement between parts of the spin network that describes its horizon. We also speculate that the entropy production during the black hole creation and evaporation is actually an expression of entanglement between gravity and matter.