Generalizing Entanglement

The expected indefinite causal structure in quantum gravity poses a challenge to the notion of entanglement: If two parties are in an indefinite causal relation of being spacelike and timelike, can they still be entangled? If so, how does one measure the amount of entanglement? We propose to generalize the notions of entanglement and entanglement measure to address these questions. Incidentally but importantly, the generalization opens the path to study quantum entanglement of states, channels, networks and processes with definite or indefinite causal structure in a unified fashion, e.g., we show that the entanglement distillation capacity of a state, the quantum communication capacity of a channel, and the entanglement generation capacity of a network or a process are different manifestations of one and the same entanglement measure.