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We investigate the quantum Cramer-Rao bounds on the joint multiple-parameter estimation with the Gaussian state as a probe.
- We derive the explicit right logarithmic derivative and symmetric logarithmic derivative operators in such a situation.
- We compute the corresponding quantum Fisher information matrices, and find that they can be fully expressed in terms of the mean displacement and covariance matrix of the Gaussian state.
- Finally, we give some examples to show the utility of our analytical results.
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