內容：

The usual way to reveal properties of an unknown quantum state, given many copies of a system in that state, is to perform measurements of dierent observables and to analyse the results statistically1,2. For non-sparse but low-rank quantum states, revealing eigenvectors and corresponding eigenvalues in classical form scales super-linearly with the system dimension3–6. Here we show that multiple copies of a quantum system with density matrix  can be used to construct the unitary transformation e

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