| Autor: |
Goldberg AZ; National Research Council of Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6, Canada.; Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada., Sánchez-Soto LL; Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain.; Max-Planck-Institute für die Physik des Lichts, 91058 Erlangen, Germany., Ferretti H; Department of Physics, University of Toronto, 60 St. George Street, Toronto, Ontario M5S 1A7, Canada. |
| Abstrakt: |
The quantum Cramér-Rao bound is a cornerstone of modern quantum metrology, as it provides the ultimate precision in parameter estimation. In the multiparameter scenario, this bound becomes a matrix inequality, which can be cast to a scalar form with a properly chosen weight matrix. Multiparameter estimation thus elicits trade-offs in the precision with which each parameter can be estimated. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix as the metric tensor linked to the geometry of the underlying algebra su(n), with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization. |
