An upper bound on the number of compatible parameters in simultaneous quantum estimation
arXiv:1910.10917 · doi:10.1088/1751-8121/ab6d3d
Abstract
Simultaneous estimation of multiple parameters is required in many practical applications. A lower bound on the variance of simultaneous estimation is given by the quantum Fisher information matrix. This lower bound is, however, not necessarily achievable. There exists a necessary and sufficient condition for its achievability. It is unknown how many parameters can be estimated while satisfying this condition. In this paper, we analyse an upper bound on the number of such parameters through linear-algebraic techniques. This upper bound depends on the algebraic structure of the quantum system used as a probe. We explicitly calculate this bound for two quantum systems: single qubit and two-qubit X-states.
arXiv comment17 pages
References in corpus (28)
- Quantum sensing
- Quantum metrology
- Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
- Quantum discord for two-qubit X-states
- Quantum Fisher information matrix and multiparameter estimation
- Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement
- Generalized Limits for Single-Parameter Quantum Estimation
- Quantum Enhanced Multiple Phase Estimation
- Quantum Enhancement of the Zero-Area Sagnac Interferometer Topology for Gravitational Wave Detection
- Compatibility in Multiparameter Quantum Metrology
- Quantum enhanced estimation of a multi-dimensional field
- A new approach to the Cramer-Rao type bound of the pure state model
- Quantum Fisher information of entangled coherent state in the presence of photon losses: exact solution
- Sensitivity Bounds for Multiparameter Quantum Metrology
- Evaluating the Holevo Cramér-Rao bound for multi-parameter quantum metrology
- Quantum fisher information in noninertial frames
- Optimal measurements for quantum multiparameter estimation with general states
- Quantum thermometry by single-qubit dephasing
- Optimal control for one-qubit quantum sensing
- Quantum probes for the cutoff frequency of Ohmic environments
- Bounds on Quantum Multiple-Parameter Estimation with Gaussian State
- Enhancing parameter precision of optimal quantum estimation by direct quantum feedback
- Classification and characterization of quantum parametric models in quantum estimation theory
- Multiple phase estimation for arbitrary pure states under white noise
- Maximal quantum Fisher information for general su(2) parametrization processes
- Fisher information of a squeezed-state interferometer with a finite photon-number resolution
- Parameter estimation for an expanding universe
- Optimal control for multi-parameter quantum estimation with time-dependent Hamiltonians