  In this paper, the following scenario is considered: there are two qubits
possessed by two parties at different locations. Qubits have been prepared in
one of a maximum of four, mutually-orthogonal, entangled states and the parties
wish to distinguish between the states by using local operations and classical
communication. Although in general it is not possible to distinguish between
four arbitrary states, the parties can spend some pre-shared entanglement to
achieve perfect discrimination between four qubit states and can also preserve
the entanglement of the states after discrimination. This is shown by employing
the theory of majorization and the connections between entanglement
transformations and state discrimination protocols.
