B. M. Escher, L. Davidovich, N. Zagury, R. L. de Matos Filho
The minimum achievable statistical error in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase- shifts under phase diffusion, which shows that the estimation error cannot be smaller than a noise- dependent constant.
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http://arxiv.org/abs/1207.3307
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