Designing optimal protocols in Bayesian quantum parameter estimation with higher-order operations
arXiv:2311.01513 · doi:10.1103/PhysRevResearch.6.023305
Abstract
Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal protocol, i.e., the most precise one. It has been solved for some specific instances of the problem, but in general even numerical methods are not known. Here, we focus on the single-shot Bayesian setting, where the goal is to find the optimal initial state of the probe (which can be entangled with an auxiliary system), the optimal measurement, and the optimal estimator function. We leverage the formalism of higher-order operations to develop a method based on semidefinite programming that finds a protocol that is close to the optimal one with arbitrary precision. Crucially, our method is not restricted to any specific quantum evolution, cost function or prior distribution, and thus can be applied to any estimation problem. Moreover, it can be applied to both single or multiparameter estimation tasks. We demonstrate our method with three examples, consisting of unitary phase estimation, thermometry in a bosonic bath, and multiparameter estimation of an SU(2) transformation. Exploiting our methods, we extend several results from the literature. For example, in the thermometry case, we find the optimal protocol at any finite time and quantify the usefulness of entanglement.
Now the thermometry example also involves the mean-square logarithmic error (see the Appendix). Close to the published version!
References in corpus (43)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- Separability Criterion for Density Matrices
- Quantum sensing
- Advances in Quantum Metrology
- Quantum metrology
- GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
- Nanometer scale quantum thermometry in a living cell
- Optical Magnetometry
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Reference frames, superselection rules, and quantum information
- Quantum metrology from a quantum information science perspective
- Super-resolving phase measurements with a multi-photon entangled state
- The elusive Heisenberg limit in quantum enhanced metrology
- The European Quantum Technologies Roadmap
- Theoretical framework for quantum networks
- Quantum noise limited and entanglement-assisted magnetometry
- Quantum Circuits Architecture
- Distinguishing separable and entangled states
- Transforming quantum operations: quantum supermaps
- Individual quantum probes for optimal thermometry
- Optimal states and almost optimal adaptive measurements for quantum interferometry
- Achieving the Heisenberg limit in quantum metrology using quantum error correction
- Multi-parameter estimation beyond Quantum Fisher Information
- Thermometry in the quantum regime: Recent theoretical progress
- Classical randomness in quantum measurements
- Memory effects in quantum channel discrimination
- Adaptive quantum metrology under general Markovian noise
- Quantum metrology with full and fast quantum control
- Single-qubit thermometry
- Bayesian quantum frequency estimation in presence of collective dephasing
- Single-atom quantum probes for ultracold gases using nonequilibrium spin dynamics
- Process POVM: A mathematical framework for the description of process tomography experiments
- Quantum metrology for non-Markovian processes
- Semidefinite Programming in Quantum Information Science
- Beyond quantum Fisher information: optimal phase estimation with arbitrary a priori knowledge
- QuanEstimation: An open-source toolkit for quantum parameter estimation
- Frequentist and Bayesian Quantum Phase Estimation
- Optimal Strategies of Quantum Metrology with a Strict Hierarchy
- Fundamental limits in Bayesian thermometry and attainability via adaptive strategies
- Optimal and Variational Multi-Parameter Quantum Metrology and Vector Field Sensing
- Unitary channel discrimination beyond group structures: Advantages of sequential and indefinite-causal-order strategies
- Optimal nonequilibrium thermometry in Markovian environments
- Quantum scale estimation
Cited by in corpus (14)
- Current Trends in Global Quantum Metrology
- Fully-Optimized Quantum Metrology: Framework, Tools, and Applications
- Strict hierarchy of optimal strategies for global estimations: Linking global estimations with local ones
- Interplay between time and energy in bosonic noisy quantum metrology
- First-principles construction of symmetry-informed quantum metrologies
- Metrological symmetries in singular quantum multi-parameter estimation
- Model-aware reinforcement learning for high-performance Bayesian experimental design in quantum metrology
- On the role of symmetry and geometry in global quantum sensing
- Retrieving maximum information of symmetric states from their corrupted copies
- Quantifying information flow in quantum processes
- Bayesian quantum phase estimation with fixed photon states
- Selective and noise-resilient wave estimation with quantum sensor networks
- Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
- Adaptive, symmetry-informed Bayesian metrology for precise quantum technology measurements