Seth Lloyd, Masoud Mohseni, Patrick Rebentrost
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 different observables and to analyze the measurement results statistically. Here we show that the unknown quantum state can play an active role in its own analysis. In particular, given multiple copies of a quantum system with density matrix R, then it is possible to perform the unitary transformation e^{-i R t}. As a result, one can create quantum coherence among different copies of the system to perform `quantum self analysis,' revealing the eigenvectors and eigenvalues of the unknown state in time exponentially faster than any existing algorithm.
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http://arxiv.org/abs/1307.0401
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