Finding the optimal probe state for multiparameter quantum metrology using conic programming
arXiv:2401.05886 · doi:10.1038/s41534-024-00905-x
Abstract
The aim of the channel estimation is to estimate the parameters encoded in a quantum channel. For this aim, it is allowed to choose the input state as well as the measurement to get the outcome. Various precision bounds are known for the state estimation. For the channel estimation, the respective bounds are determined depending on the choice of the input state. However, determining the optimal input probe state and the corresponding precision bounds in estimation is a non-trivial problem, particularly in the multi-parameter setting, where parameters are often incompatible. In this paper, we present a conic programming framework that allows us to determine the optimal probe state for the corresponding multi-parameter precision bounds. The precision bounds we consider include the Holevo-Nagaoka bound and the tight precision bound that give the optimal performances of correlated and uncorrelated measurement strategies, respectively. Using our conic programming framework, we discuss the optimality of a maximally entangled probe state in various settings. We also apply our theory to analyze the canonical field sensing problem using entangled quantum probe states.
arXiv comment36 pages, 2 columns, 5 figures. Title change, added references, and edited introduction
References in corpus (30)
- General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
- Quantum metrology from a quantum information science perspective
- The elusive Heisenberg limit in quantum enhanced metrology
- A complete family of separability criteria
- Imaging with quantum states of light
- Distinguishing separable and entangled states
- Statistical distinguishability between unitary operations
- Quantum enhanced estimation of a multi-dimensional field
- Bosonic Quantum Codes for Amplitude Damping
- Optimal discrimination of quantum operations
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Fundamental limits to quantum channel discrimination
- Attaining the ultimate precision limit in quantum state estimation
- Amortized Channel Divergence for Asymptotic Quantum Channel Discrimination
- Permutation-invariant quantum codes
- Discrimination of two channels by adaptive methods and its application to quantum system
- The power of symmetric extensions for entanglement detection
- Comparison between the Cramer-Rao and the mini-max approaches in quantum channel estimation
- Quantum metrology for non-Markovian processes
- Asymptotic theory of quantum channel estimation
- Optimal quantum codes for preventing collective amplitude damping
- Efficient computation of the Nagaoka--Hayashi bound for multi-parameter estimation with separable measurements
- Optimal Strategies of Quantum Metrology with a Strict Hierarchy
- Ultimate limits for multiple quantum channel discrimination
- Optimal probes and error-correction schemes in multi-parameter quantum metrology
- Tight Cramér-Rao type bounds for multiparameter quantum metrology through conic programming
- Generalized quantum process discrimination problems
- Finite-round quantum error correction on symmetric quantum sensors
- Attainability of the Holevo-Cramér-Rao bound for two-qubit 3D magnetometry
- Multiparameter estimation with two qubit probes in noisy channels
Cited by in corpus (6)
- Simultaneous optical phase and loss estimation revisited: measurement and probe incompatibility
- Indefinite causal order strategy does not improve the estimation of group action
- Precision Bounds for Characterising Quantum Measurements
- Optimal quantum metrology under energy constraints
- QMetro++ -- Python optimization package for large scale quantum metrology with customized strategy structures
- Measurement compatibility in multiparameter quantum interferometry