  Quantum state elimination measurements tell us what states a quantum system
does not have. This is different from state discrimination, where one tries to
determine what the state of a quantum system is, rather than what it is not.
Apart from being of fundamental interest, quantum state elimination may find
uses in quantum communication and quantum cryptography. We consider unambiguous
quantum state elimination for two or more qubits, where each qubit can be in
one of two possible states. Optimal measurements for eliminating one and two
states out of four two-qubit states are given. We also prove that if we want to
maximise the average number of eliminated overall N-qubit states, then
individual measurements on each qubit are optimal.
