Quantum information entropy, often referred to as quantum entropy or von Neumann entropy, is a concept in quantum mechanics that measures the amount of uncertainty or information content associated with a quantum state. It is a measure of the "mixedness" or "disorder" of a quantum system.
In the context of black holes, quantum information entropy is related to the information that can be stored on the surface area of the event horizon. This connection arises from the holographic principle, which suggests that the information content of a region in spacetime can be encoded on its boundary.
According to the holographic principle, the information within a black hole can be represented by the degrees of freedom on its event horizon, which acts as a boundary. The surface area of the event horizon is directly related to the entropy of the black hole. Specifically, the entropy of a black hole is proportional to one-quarter of its event horizon area, as formulated by Jacob Bekenstein and further developed by Stephen Hawking.
This relationship between the entropy and surface area of the event horizon is significant because it implies that the information content of a black hole is not determined solely by its volume but also by the characteristics of its boundary. It suggests a deep connection between gravity, quantum mechanics, and information theory.
The study of this relationship between quantum information entropy, black holes, and the holographic principle is an active area of research in theoretical physics, particularly in the field of quantum gravity and string theory.