  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.
