A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single-qubit states

We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace and (ii) qubits prepared in almost any three different (potentially highly mixed) states. In some sense this measurement is a 'more universal' dynamical element than a universal two-qubit unitary gate, since the latter must be supplemented by measurement. Because of the rotational invariance of the measurement used, our scheme is robust to collective decoherence in a manner very different to previous proposals—in effect it is only ever sensitive to the relational properties of the qubits.