Simple expression for the quantum Fisher information matrix
arXiv:1801.00945 · doi:10.1103/PhysRevA.97.042322
Abstract
Quantum Fisher information matrix (QFIM) is a cornerstone of modern quantum metrology and quantum information geometry. Apart from optimal estimation, it finds applications in description of quantum speed limits, quantum criticality, quantum phase transitions, coherence, entanglement, and irreversibility. We derive a surprisingly simple formula for this quantity, which, unlike previously known general expression, does not require diagonalization of the density matrix, and is provably at least as efficient. With a minor modification, this formula can be used to compute QFIM for any finite-dimensional density matrix. Because of its simplicity, it could also shed more light on the quantum information geometry in general.
arXiv comment4+1 pages, v2: proof simplified, introduction extended, added discussion and examples
References in corpus (59)
- Observation of Gravitational Waves from a Binary Black Hole Merger
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- Quantum metrology
- Enhancing the sensitivity of the LIGO gravitational wave detector by using squeezed states of light
- Ultimate physical limits to computation
- The maximum speed of dynamical evolution
- The elusive Heisenberg limit in quantum enhanced metrology
- A quantum network of clocks
- Quantum Metrology in Non-Markovian Environments
- Fidelity approach to quantum phase transitions
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Measurement of stimulated Hawking emission in an analogue system
- Quantum speed limit for physical processes
- Quantum critical scaling of the geometric tensors
- Quantum speed limits in open system dynamics
- Quantacell: Powerful charging of quantum batteries
- Quantum noise limited and entanglement-assisted magnetometry
- Quantum Enhanced Multiple Phase Estimation
- Measuring multipartite entanglement via dynamic susceptibilities
- Quantum phase estimation with lossy interferometers
- Individual quantum probes for optimal thermometry
- Quantum sensing with arbitrary frequency resolution
- Quantum fidelity for arbitrary Gaussian states
- Generalized Geometric Quantum Speed Limits
- Quantum parameter estimation using general single-mode Gaussian states
- Quantum parameter estimation using general single-mode Gaussian states
- General optimality of the Heisenberg limit for quantum metrology
- Optimal measurements for simultaneous quantum estimation of multiple phases
- Far-field Superresolution of Thermal Electromagnetic Sources at the Quantum Limit
- Optimal quantum estimation of the Unruh-Hawking effect
- Bures volume of the set of mixed quantum states
- Optimal phase measurements with pure Gaussian states
- Fundamental quantum interferometry bound for the squeezed-light-enhanced gravitational-wave detector GEO600
- Analogue Hawking Radiation in a dc-SQUID Array Transmission Line
- Discontinuities of the quantum Fisher information and the Bures metric
- Bures metric over thermal state manifolds and quantum criticality
- Quantum Thermal Machine as a Thermometer
- Ultimate sensitivity of precision measurements with Gaussian quantum light : a multi-modal approach
- Chemical compass model for avian magnetoreception as a quantum coherent device
- Quantum information-geometry of dissipative quantum phase transitions
- Measurement of damping and temperature: Precision bounds in Gaussian dissipative channels
- Note on Explicit Formulae for the Bures Metric
- Optimal probe states for the estimation of Gaussian unitary channels
- Phase estimation for thermal Gaussian states
- Bounds on Quantum Multiple-Parameter Estimation with Gaussian State
- Squeezed vacuum as a universal quantum probe
- Heisenberg scaling in Gaussian quantum metrology
- Squeezing Inequalities and Entanglement for Identical Particles
- Fisher information approach to non-equilibrium phase transitions in quantum XXZ spin chain with boundary noise
- Entanglement is not very useful for estimating multiple phases
- Bures distance between two displaced thermal states
- Optimal quantum states for frequency estimation
- Experimental test of photonic entanglement in accelerated reference frames
- Optimal estimation of squeezing
- Criterion on remote clocks synchronization within a Heisenberg scaling accuracy
- Fitting magnetic field gradient with Heisenberg-scaling accuracy
- Optimizing phase estimation algorithms for diamond spin magnetometry
- Quantum limited measurement of space-time curvature with scaling beyond the conventional Heisenberg limit
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- Quantum limited superresolution of an incoherent source pair in three dimensions
- QuanEstimation: An open-source toolkit for quantum parameter estimation
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- A dynamical approach to ancilla assisted quantum thermometry
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- Bidirectional Teleportation using Fisher Information
- Quantum States, Groups and Monotone Metric Tensors
- On the optimality of the radical-pair quantum compass
- Monitoring variations of refractive index via Hilbert-Schmidt speed and applying this phenomenon to improve quantum metrology
- Untwining multiple parameters at the exclusive zero-coincidence points with quantum control
- Multiparameter estimation with two qubit probes in noisy channels
- Universal adversarial perturbations for multiple classification tasks with quantum classifiers
- Parameter estimation via indefinite causal structures
- Quantum-enhanced mean value estimation via adaptive measurement
- Quantum Limits on Localizing Point Objects against a Uniformly Bright Disk
- Persistent quantum advantage with definite photon-number states in lossy multiple-phase estimation
- Iterative optimization in quantum metrology and entanglement theory using semidefinite programming
- Lee-Yang zeros and quantum Fisher information matrix in a nonlinear system
- Information Geometry, Jordan Algebras, and a Coadjoint Orbit-Like Construction
- Ultimate Quantum Precision Limit at Colliders: Conditions and Case Studies
- G-dual teleparallel connections in Information Geometry
- Quantum Fisher information from tensor network integration of Lyapunov equation
- Precision Bounds for Characterising Quantum Measurements
- Interradical motion can push magnetosensing precision towards quantum limits
- Metrological approach to the emergence of classical objectivity
- Multiparameter quantum metrology with postselection measurements
- Enhancement of quantum sensing in a dissipatively coupled two-mode system
- Spontaneous Scattering of Raman Photons from Cavity-QED Systems in the Ultrastrong Coupling Regime
- Information geometry of nonmonotonic quantum natural gradient