Abstract
The score operators of a quantum system are the symmetric logarithmic derivatives of the system's parametrically defined quantum state. Score operators are central to the calculation of the quantum Fisher information (QFI) associated with the state of the system, and the QFI determines the maximum precision with which the state parameters can be estimated. We give a simple, explicit expression for score operators of a qubit and apply this expression in a series of settings. We treat in detail the task of identifying a quantum Pauli channel from the state of its qubit output, and we show that a "balanced" probe state is highly robust for this purpose. The QFI for this task is a matrix, and we study its determinant, for which we establish a Cramer-Rao inequality.
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