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We prove that universal quantum computation is possible using only (i) thephysically natural measurement on two qubits which distinguishes the singletfrom the triplet subspace, and (ii) qubits prepared in almost any threedifferent (potentially highly mixed) states. In some sense this measurement isa `more universal' dynamical element than a universal 2-qubit unitary gate,since the latter must be supplemented by measurement. Because of the rotationalinvariance of the measurement used, our scheme is robust to collectivedecoherence in a manner very different to previous proposals - in effect it isonly ever sensitive to the relational properties of the qubits.Comment: TR apologises for yet again finding a coauthor with a ridiculous  middle name [12

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