Mutual Information Bounded by Fisher Information
arXiv:2403.10248 · doi:10.1103/PhysRevResearch.7.L022013
Abstract
We derive a general upper bound to mutual information in terms of the Fisher information. The bound may be further used to derive a lower bound for the Bayesian quadratic cost. These two provide alternatives to other inequalities in the literature (e.g.~the van Trees inequality) that are useful also for cases where the latter ones give trivial bounds. We then generalize them to the quantum case, where they bound the Holevo information in terms of the quantum Fisher information. We illustrate the usefulness of our bounds with a case study in quantum phase estimation. Here, they allow us to adapt to mutual information (useful for global strategies where the prior plays an important role) the known and highly nontrivial bounds for the Fisher information in the presence of noise. The results are also useful in the context of quantum communication, both for continuous and discrete alphabets.
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References in corpus (34)
- Quantum sensing
- Advances in Quantum Metrology
- Quantum metrology
- Quantum metrology with nonclassical states of atomic ensembles
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- Advances in Photonic Quantum Sensing
- The elusive Heisenberg limit in quantum enhanced metrology
- Entropic Uncertainty Relations and their Applications
- Squeezed states of light and their applications in laser interferometers
- Using entanglement against noise in quantum metrology
- Efficient tools for quantum metrology with uncorrelated noise
- Adaptive quantum metrology under general Markovian noise
- Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
- Phase estimation without a priori knowledge in the presence of loss
- Ancilla-free quantum error correction codes for quantum metrology
- Does nonlinear metrology offer improved resolution? Answers from quantum information theory
- -Corrected Heisenberg Limit
- Universality of the Heisenberg limit for estimates of random phase shifts
- Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
- Asymptotic theory of quantum channel estimation
- Using adaptiveness and causal superpositions against noise in quantum metrology
- Bayesian estimation for quantum sensing in the absence of single-shot detection
- Minimax and adaptive estimation of the Wigner function in quantum homodyne tomography with noisy data
- Bayesian Quantum Multiphase Estimation Algorithm
- Bayesian parameter estimation using Gaussian states and measurements
- Squeezing metrology: a unified framework
- Multiple-phase quantum interferometry -- real and apparent gains of measuring all the phases simultaneously
- Information geometry under hierarchical quantum measurement
- Digital Quantum Estimation
- Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
- A protocol for global multiphase estimation
- Discrete-to-continuous transition in quantum phase estimation
- Physics-inspired forms of the Bayesian Cramér-Rao bound