 Solution

A pure bipartite quantum state is entangled if it cannot be written as a tensor product $|a⟩\otimes |b⟩$. More generally a mixed quantum state is entangled if its density matrix cannot be expressed as a convex mixture of product density matrices. Two applications are quantum teleportation, which transfers an unknown qubit using a shared entangled pair plus classical communication, and superdense coding, which uses a shared entangled pair and transmission of one qubit to communicate two classical bits. Neither permits faster-than-light communication.