Related papers: Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology

URL: http://arxiv.org/abs/2105.04568v2
Date: Thu, 9 Sep 2021 18:13:23 GMT
Title: Intrinsic Sensitivity Limits for Multiparameter Quantum Metrology
Authors: Aaron Z. Goldberg, Luis L. S\'anchez-Soto, and Hugo Ferretti
Abstract summary: The quantum Cram'er-Rao bound provides the ultimate precision in parameter estimation. We show that, if the information is encoded in a unitary transformation, we can naturally choose the weight matrix. This ensures an intrinsic bound that is independent of the choice of parametrization.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: The quantum Cram\'er-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 tradeoffs 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 $\mathfrak{su}(n)$, with applications in numerous fields. This ensures an intrinsic bound that is independent of the choice of parametrization.

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