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We show how to prepare a single molecular ion in a specific internal quantumstate in a situation where the molecule is trapped and sympathetically cooledby an atomic ion and where its internal degrees of freedom are initially inthermal equilibrium with the surroundings. The scheme is based on conditionalcreation of correlation between the internal state of the molecule and thetranslational state of the collective motion of the two ions, followed by aprojection measurement of this collective mode by atomic ion shelvingtechniques. State preparation in a large number of internal states is possible.Comment: 4 pages, 2 figures, 2 table

Probabilistic state preparation of a single molecular ion by projection measurement