Abstract.
We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the maximal sensitivity that can be achieved for any of the pure states from which the initial density matrix is mixed. This provides a very general proof that purely classical correlations cannot improve the sensitivity of parameter estimation schemes in quantum enhanced measurement schemes.
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Braun, D. Parameter estimation with mixed quantum states. Eur. Phys. J. D 59, 521–523 (2010). https://doi.org/10.1140/epjd/e2010-00195-3
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DOI: https://doi.org/10.1140/epjd/e2010-00195-3