Quantum Fisher information from randomized measurements
Résumé
The quantum Fisher information (QFI) is a fundamental quantity of interest in many areas from quantum metrology to quantum information theory. It can in particular be used as a witness to establish the degree of multi-particle entanglement in quantum many-body-systems. In this work, we use polynomials of the density matrix to construct monotonically increasing lower bounds that converge to the QFI. Using randomized measurements we propose a protocol to accurately estimate these lower bounds in state-of-art quantum technological platforms. We perform numerical analysis to obtain the number of measurements required to overcome statistical errors for the lower bound estimates and provide two examples of applications of the method in quantum systems made of coupled qubits and collective spins.
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