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The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. The quantum Fisher information of a state with respect to the observable is defined as where and are the eigenvalues and eigenvectors of the density matrix respectively, and the summation goes over all and such that . When the observable generates a unitary transformation of the system with a parameter from initial state , where is the number of independent repetitions.

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  • Quantum Fisher information (en)
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  • The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. The quantum Fisher information of a state with respect to the observable is defined as where and are the eigenvalues and eigenvectors of the density matrix respectively, and the summation goes over all and such that . When the observable generates a unitary transformation of the system with a parameter from initial state , where is the number of independent repetitions. (en)
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  • The quantum Fisher information is a central quantity in quantum metrology and is the quantum analogue of the classical Fisher information. The quantum Fisher information of a state with respect to the observable is defined as where and are the eigenvalues and eigenvectors of the density matrix respectively, and the summation goes over all and such that . When the observable generates a unitary transformation of the system with a parameter from initial state , the quantum Fisher information constrains the achievable precision in statistical estimation of the parameter via the quantum Cramér–Rao bound as where is the number of independent repetitions. It is often desirable to estimate the magnitude of an unknown parameter that controls the strength of a system's Hamiltonian with respect to a known observable during a known dynamical time . In this case, defining , so that , means estimates of can be directly translated into estimates of . (en)
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