In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper, we investigate two SU(2) TPT models and propose the singular behavior of the quantum metric tensor around the TPT point as a tool for the simultaneous optimal estimation of multiple parameters. We find that the proposed TPT sensing protocol can achieve the same metrology performance as the quantum-control-enhanced one. Moreover, the probe state of the TPT sensing protocol is only the ground state of the Hamiltonian rather than the entangled state required in the control-enhanced one. In addition, an adaptive multiparameter estimation strategy is developed for updating the estimated values until the desired quantum Cram\'er-Rao bound is approached. Our work reinforces the connection between quantum multiparameter estimation and topology physics, with potential inspiration for quantum critical metrology.In quantum multiparameter estimation, multiple to-be-estimated parameters are encoded in a quantum dynamics system by a unitary evolution. As the parameters vary, the system may undergo a topological phase transition (TPT). In this paper, we investigate two SU(2) TPT models and propose the singular behavior of the quantum metric tensor around the TPT point as a tool for the simultaneous optimal estimation of multiple parameters. We find that the proposed TPT sensing protocol can achieve the same metrology performance as the quantum-control-enhanced one. Moreover, the probe state of the TPT sensing protocol is only the ground state of the Hamiltonian rather than the entangled state required in the control-enhanced one. In addition, an adaptive multiparameter estimation strategy is developed for updating the estimated values until the desired quantum Cram\'er-Rao bound is approached. Our work reinforces the connection between quantum multiparameter estimation and topology physics, with potential inspiration for quantum critical metrology.

arXiv:2402.07089Physical Review AFeb 9, 202410 citations

Multiparameter Quantum Metrology in Molecular Dimers

Omar Bachain, Mohamed Amazioug, Rachid Ahl Laamara

We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature $T$ and detuning $Λ$ . By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature $T$ and detuning $Λ$. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.

quant-pharXiv:2607.11831Jul 14, 20260 citations

A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging

Francesco Albarelli, Marco Barbieri, Marco G. Genoni +1 more

arXiv:1911.12067Physics Letters AFeb 6, 2020217 citations

Quantum-error-correction-inspired multiparameter quantum metrology

Sivaprasad Omanakuttan, Jonathan A. Gross, Tyler J. Volkoff

Physical Review AJun 3, 20260 citations

Fisher-information susceptibility for multiparameter quantum estimation

Francesco Albarelli, Ilaria Gianani, Marco G. Genoni +1 more

Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher-information measurement noise susceptibility now allows one to quantify the robustness of measurement for single-parameter estimation. Here we extend this notion to the multiparameter quantum estimation scenario. We provide its mathematical definition in the form of a semidefinite program. Although a closed formula could not be found, we further derive an upper and a lower bound to the susceptibility. We then apply these techniques to two paradigmatic examples of multiparameter estimation: the joint estimation of phase and phase diffusion and the estimation of the different parameters describing the incoherent mixture of optical point sources. Our figure of merit provides clear indications on conditions allowing or hampering robustness of multiparameter measurements.Noise affects the performance of quantum technologies, hence the importance of elaborating operative figures of merit that can capture its impact in exact terms. In quantum metrology, the introduction of the Fisher-information measurement noise susceptibility now allows one to quantify the robustness of measurement for single-parameter estimation. Here we extend this notion to the multiparameter quantum estimation scenario. We provide its mathematical definition in the form of a semidefinite program. Although a closed formula could not be found, we further derive an upper and a lower bound to the susceptibility. We then apply these techniques to two paradigmatic examples of multiparameter estimation: the joint estimation of phase and phase diffusion and the estimation of the different parameters describing the incoherent mixture of optical point sources. Our figure of merit provides clear indications on conditions allowing or hampering robustness of multiparameter measurements.

arXiv:2312.02035Physical Review ASep 26, 20246 citations

QUANTUM METROLOGY AND SIMULATION

Jacob M. Taylor

Dalgarno Celebratory SymposiumNov 1, 20090 citations

We investigate multiparameter quantum estimation in a molecular dimer composed of two dipole--dipole interacting two-level systems, focusing on the simultaneous estimation of temperature

T

and detuning

Λ

. By employing a vectorization approach to derive the quantum Fisher information matrix, we analyze the precision limits of both simultaneous and individual estimation strategies. We show that simultaneous estimation outperforms the individual one in the near-resonant and low-temperature regime, where quantum coherence is enhanced, while its advantage is progressively reduced under detuned conditions and increasing temperature. Our results demonstrate that temperature acts as a key control parameter governing both estimation precision providing a unified perspective on quantum metrology. These findings highlight the potential of molecular quantum systems as realistic platforms for multiparameter quantum sensing.