For two orthogonal black-box n-qubit states, a poly(n, 1/ε)-size approximating unitary exists that maps basis states to them while resetting all auxiliaries on every input.
Gentle Measurement of Quant um States and Differential Privacy
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Approximating Unitary Preparations of Orthogonal Black Box States
For two orthogonal black-box n-qubit states, a poly(n, 1/ε)-size approximating unitary exists that maps basis states to them while resetting all auxiliaries on every input.