= Solution
A pure bipartite <quantum state> is <entangled> if it cannot be written as a <tensor product> $|a\rangle\otimes|b\rangle$. 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.
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