Noisy Metrology: A saturable lower bound on quantum Fisher information

Abstract

In order to provide a guaranteed precision and a more accurate judgement about the true value of the Cramér-Rao bound and its scaling behavior, an upper bound (equivalently a lower bound on the quantum Fisher information) for precision of estimation is introduced. Unlike the bounds previously introduced in the literature, the upper bound is saturable and yields a practical instruction to estimate the parameter through preparing the optimal initial state and optimal measurement. The bound is based on the underling dynamics and its calculation is straightforward and requires only the matrix representation of the quantum maps responsible for encoding the parameter. This allows us to apply the bound to open quantum systems whose dynamics are described by either semigroup or non-semigroup maps. Reliability and efficiency of the method to predict the ultimate precision limit are demonstrated by {three} main examples.

7 pages, 2 figures

References in corpus (8)

• 14-qubit entanglement: creation and coherence
• Optimal Quantum Phase Estimation
• 'Designer atoms' for quantum metrology
• The ultimate precision limits for noisy frequency estimation
• Quantum Metrological Limits via a Variational Approach
• Nonlinear quantum metrology of many-body open systems
• Practical Quantum Metrology in Noisy Environments
• Enhancement of Frequency Estimation by Spatially Correlated Environments

Cited by in corpus (5)

• Nonlinear quantum metrology of many-body open systems
• Estimating phase with a random generator: Strategies and resources in multiparameter quantum metrology
• Improving the precision of frequency estimation via long-time coherences
• Control-enhanced quantum metrology under Markovian noise
• Optimal quantum precision in noise estimation: Is entanglement necessary?