From qubits to black holes: Entropy, entanglement and all that

Entropy plays a crucial role in the characterization of information and entanglement, but it is not a scalar quantity and for many systems it is different for different relativistic observers. We discuss two examples: entropy of a single qubit and renormalized entropy as given by a uniformly accelerated observer. Loop quantum gravity predicts the Bekenstein-Hawking term for black hole entropy and the logarithmic correction to it. The latter originates in the entanglement between the pieces of spin networks that describe black hole horizon. Entanglement between gravity and matter may restore the unitarity in the black hole evaporation process. If the collapsing matter is assumed to be initially in a pure state, then entropy of the Hawking radiation is exactly the created entanglement between matter and gravity.