A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
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Probabilistic and approximate universal quantum purification machines
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.