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Quantum metrology with unitary parametrization processes

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arxiv 1409.4057 v2 pith:WIEJJ7IU submitted 2014-09-14 quant-ph

Quantum metrology with unitary parametrization processes

classification quant-ph
keywords quantuminformationfisherrepresentationmetrologyparametrizationexpressioninitial
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Furthermore, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation in the last.

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