Quantum Fisher information on two manifolds of two-mode Gaussian states
arXiv:1605.06524 · doi:10.1103/PhysRevA.93.052330
Abstract
We investigate two special classes of two-mode Gaussian states of light that are important from both the experimental and theoretical points of view: the mode-mixed thermal states and the squeezed thermal ones. Aiming to a parallel study, we write the Uhlmann fidelity between pairs of states belonging to each class in terms of their defining parameters. The quantum Fisher information matrices on the corresponding four-dimensional manifolds are diagonal and allow insightful parameter estimation. The scalar curvatures of the Bures metric on both Riemannian manifolds of special two-mode Gaussian states are evaluated and discussed. They are functions of two variables, namely, the mean numbers of photons in the incident thermal modes. Our comparative analysis opens the door to further investigation of the interplay between geometry and statistics for Gaussian states produced in simple optical devices.
References in corpus (23)
- Gaussian Quantum Information
- Inseparability criterion for continuous variable systems
- Continuous variable quantum information: Gaussian states and beyond
- Noncommuting mixed states cannot be broadcast
- Unknown Quantum States: The Quantum de Finetti Representation
- Quantum optics in the phase space - A tutorial on Gaussian states
- Quantum parameter estimation using general single-mode Gaussian states
- Quantum parameter estimation using general single-mode Gaussian states
- Bures volume of the set of mixed quantum states
- Quantum Fisher information for states in exponential form
- Uhlmann fidelity between two-mode Gaussian states
- Fidelity for displaced squeezed states and the oscillator semigroup
- Covariance and Fisher information in quantum mechanics
- Quantum metrology for relativistic quantum fields
- Alternative fidelity measure for quantum states
- Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies
- SU(2) and SU(1,1) algebra eigenstates: A unified analytic approach to coherent and intelligent states
- Optimal estimation of entanglement
- Bures and Statistical Distance for Squeezed Thermal States
- Information geometry of Gaussian channels
- Gaussian interferometric power
- Bures distance between two displaced thermal states
- Hellinger distance as a measure of Gaussian discord
Cited by in corpus (21)
- Quantum Fisher information matrix and multiparameter estimation
- A Geometric Perspective on Quantum Parameter Estimation
- Multiparameter Gaussian Quantum Metrology
- Estimation of Gaussian quantum states
- Entanglement-Based Quantum Information Technology
- Review: Quantum Metrology and Sensing with Many-Body Systems
- Practical route to entanglement-assisted communication over noisy bosonic channels
- Ultimate accuracy limit of quantum pulse-compression ranging
- Demonstration of Entanglement-Enhanced Covert Sensing
- Physical-Layer Supervised Learning Assisted by an Entangled Sensor Network
- Renyi relative entropies of quantum Gaussian states
- Optimal Quantum Metrology of Distant Black Bodies
- Local geometry and quantum geometric tensor of mixed states
- Quantum Metrology of Absorption and Gain Parameters using Two-Mode Bright Squeezed Light
- Nonclassical steering and the Gaussian steering triangoloids
- Quantum advantage of time-reversed ancilla-based metrology of absorption parameters
- Bi-frequency illumination: a quantum-enhanced protocol
- Einstein-Podolsky-Rosen uncertainty limits for bipartite multimode states
- Gaussian Quantum Illumination via Monotone Metrics
- Einstein-Podolsky-Rosen-like separability indicators for two-mode Gaussian states
- Information geometry of bosonic Gaussian thermal states