Uncertainty relations between quantum Fisher information and entanglement monotones
arXiv:2501.14595 · doi:10.1103/54mc-2yl3
Abstract
Entanglement is widely regarded as an essential resource for a number of tasks and can in some cases be quantified by figures of merit related to those tasks. In quantum metrology, this is showcased by the connections between the quantum Fisher information (QFI), providing a bound to the precision, and multipartite entanglement quantifiers such as the entanglement depth. However, a connection between the QFI and entanglement monotones, i.e., functions that do not increase under Local Operations and Classical Communications, has so far remained elusive. In this work, we fill this gap by introducing a family of uncertainty relations that bound bipartite entanglement monotones from below via elements of a quantum Fisher information matrix. To further emphasize the significance of our results, we connect these relations to the achievable precision in multiparameter estimation. Considering a system split into two parts with arbitrary dimension, we also show that, while two-dimensional entanglement is sufficient to estimate a single parameter with maximal precision, genuine high-dimensional entanglement is required for multiparameter estimation. We conclude by illustrating how our method extends naturally to a multipartite splitting.
10 pages, 3 figures
References in corpus (74)
- Quantum entanglement
- Mixed State Entanglement and Quantum Error Correction
- A computable measure of entanglement
- Advances in Quantum Metrology
- Quantum-enhanced measurements: beating the standard quantum limit
- Entanglement detection
- Quantum metrology with nonclassical states of atomic ensembles
- The logarithmic negativity: A full entanglement monotone that is not convex
- Security of quantum key distribution using d-level systems
- Entanglement, Non-linear Dynamics, and the Heisenberg Limit
- Universal state inversion and concurrence in arbitrary dimensions
- Quantum metrology from a quantum information science perspective
- Quantum Fisher information matrix and multiparameter estimation
- Entanglement monotones
- Advances in High Dimensional Quantum Entanglement
- Fisher information and multiparticle entanglement
- Quantum speed limits: from Heisenberg's uncertainty principle to optimal quantum control
- Multipartite entanglement and high precision metrology
- Quantum cryptography with 3-state systems
- High-Dimensional Intra-City Quantum Cryptography with Structured Photons
- Quantum speed limit for physical processes
- A Schmidt number for density matrices
- Multi-photon entanglement in high dimensions
- Measuring multipartite entanglement via dynamic susceptibilities
- Entanglement Certification From Theory to Experiment
- Concurrence of arbitrary dimensional bipartite quantum states
- Concurrence of mixed bipartite quantum states in arbitrary dimensions
- Orbital angular momentum states enabling fiber-based high-dimensional quantum communication
- Overcoming Noise in Entanglement Distribution
- I-concurrence and tangle for isotropic states
- Quantifying entanglement resources
- The structure of multidimensional entanglement in multipartite systems
- How entangled can two couples get?
- Twisted photon entanglement through turbulent air across Vienna
- Covariance matrices and the separability problem
- Experimental GHZ Entanglement beyond Qubits
- Sensitivity Bounds for Multiparameter Quantum Metrology
- Bures volume of the set of mixed quantum states
- Extremal properties of the variance and the quantum Fisher information
- Lower bounds on concurrence and separability conditions
- Universal quantum computation with little entanglement
- Experimental high-dimensional Greenberger-Horne-Zeilinger entanglement with superconducting transmon qutrits
- Unifying several separability conditions using the covariance matrix criterion
- Experimental Preparation of High NOON States for Phonons
- Uncertainty Relation Revisited from Quantum Estimation Theory
- Multiparameter squeezing for optimal quantum enhancements in sensor networks
- Metrological Detection of Multipartite Entanglement from Young Diagrams
- Efficient entanglement criteria for discrete, continuous, and hybrid variables
- Characterizing multipartite entanglement without shared reference frames
- Entanglement cost in practical scenarios
- Entanglement Detection Beyond Measuring Fidelities
- Useful states and entanglement distillation
- Coherence, Quantum Fisher Information, Superradiance and Entanglement are Interconvertible Resources
- Quantifying entanglement with covariance matrices
- Entanglement quantification in atomic ensembles
- Characterizing entanglement dimensionality from randomized measurements
- Uncertainty relations with the variance and the quantum Fisher information based on convex decompositions of density matrices
- Experimental creation of Multi-Photon High-Dimensional Layered Quantum States
- Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin states
- Detecting and estimating continuous-variable entanglement by local orthogonal observables
- Partial transpose as a direct link between concurrence and negativity
- Observable estimation of entanglement of formation and quantum discord for bipartite mixed quantum states
- Improving sum uncertainty relations with the quantum Fisher information
- Bounding entanglement dimensionality from the covariance matrix
- Entanglement Criteria Based on Quantum Fisher Information
- Exact Quantum Fisher Matrix Results for Distributed Phases Using Multiphoton Polarization Greenberger Horne Zeilinger States
- A sufficient Entanglement Criterion Based On Quantum Fisher Information and Variance
- Alternatives of entanglement depth and metrological entanglement criteria
- Metrological usefulness of entanglement and nonlinear Hamiltonians
- Beyond i.i.d. in the Resource Theory of Asymmetry: An Information-Spectrum Approach for Quantum Fisher Information
- Quantum enhanced distributed phase sensing with a truncated SU(1,1) interferometer
- Dynamical multipartite entanglement in a generalized Tavis-Cummings model with XY spin interaction
- Characterizing high-dimensional multipartite entanglement beyond Greenberger-Horne-Zeilinger fidelities
- Quantum walk on a square lattice with identical particles