On quantumness in multi-parameter quantum estimation

Abstract

In this article we derive a measure of quantumness in quantum multi-parameter estimation problems. We can show that the ratio between the mean Uhlmann Curvature and the Fisher Information provides a figure of merit which estimates the amount of incompatibility arising from the quantum nature of the underlying physical system. This ratio accounts for the discrepancy between the attainable precision in the simultaneous estimation of multiple parameters and the precision predicted by the Cramér-Rao bound. As a testbed for this concept, we consider a quantum many-body system in thermal equilibrium, and explore the quantum compatibility of the model across its phase diagram.

21 pages, 2 Figures. arXiv admin note: text overlap with arXiv:1911.10196

References in corpus (15)

• Quantum metrology from a quantum information science perspective
• Quantum critical scaling of the geometric tensors
• Sub-millihertz magnetic spectroscopy with a nanoscale quantum sensor
• Quantum criticality as a resource for quantum estimation
• Individual quantum probes for optimal thermometry
• Quantum sensing with arbitrary frequency resolution
• Geometric phases and criticality in spin chain systems
• Optimal measurements for simultaneous quantum estimation of multiple phases
• Optimal quantum estimation of the Unruh-Hawking effect
• Bures metric over thermal state manifolds and quantum criticality
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• Fidelity approach to the disordered quantum XY model
• Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
• Symmetric Logarithmic Derivative of Fermionic Gaussian States
• The fidelity approach to the Hubbard model

Cited by in corpus (24)

• Geometry of quantum phase transitions
• Information geometry under hierarchical quantum measurement
• Nonlocal Advantages of Quantum Imaginarity
• Evading noise in multiparameter quantum metrology with indefinite causal order
• Quantum multiparameter estimation enhanced by a topological phase transition
• Generalization of Rayleigh's Criterion on Parameter Estimation with Incoherent Sources
• Metrological symmetries in singular quantum multi-parameter estimation
• Maximum logarithmic derivative bound on quantum state estimation as a dual of the Holevo bound
• Greenberger-Horne-Zeilinger state generation in qubit-chains via a single $\pi /2$-pulse
• Multiparameter estimation with two qubit probes in noisy channels
• Achieving the Multi-parameter Quantum Cramér-Rao Bound with Antiunitary Symmetry
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Randomized measurements for multi-parameter quantum metrology
• Joint optimal measurement for locating two incoherent optical point sources near the Rayleigh distance
• Dynamical multipartite entanglement in a generalized Tavis-Cummings model with XY spin interaction
• Simultaneous optical phase and loss estimation revisited: measurement and probe incompatibility
• Normal state quantum geometry, non-locality and superconductivity
• Semi-classical geometric tensor in multiparameter quantum information
• Improving quantum walk metrology with split-step quantum walk
• Optimal Displacement Sensing with Spin-Dependent Squeezed States
• Measure of set imaginarity
• Multiparameter quantum estimation with Gaussian states: efficiently evaluating Holevo, RLD and SLD Cramér-Rao bounds
• Measurement compatibility in multiparameter quantum interferometry
• Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation