Metric on the space of quantum states from relative entropy. Tomographic reconstruction
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Publication:5364951
DOI10.1088/1751-8121/aa7d7dzbMath1373.81041arXiv1612.07986OpenAlexW3099767593MaRDI QIDQ5364951
Patrizia Vitale, Vladimir I. Man'ko, Franco Ventriglia, Giuseppe Marmo
Publication date: 29 September 2017
Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.07986
Measures of information, entropy (94A17) Convex sets in (2) dimensions (including convex curves) (52A10) Convex sets and cones of operators (47L07) Quantum information, communication, networks (quantum-theoretic aspects) (81P45) Quantum state spaces, operational and probabilistic concepts (81P16)
Related Items (13)
Hamilton-Jacobi approach to potential functions in information geometry ⋮ Statistical properties of qutrit in probability representation of quantum mechanics ⋮ Information geometry, Jordan algebras, and a coadjoint orbit-like construction ⋮ Parametric models and information geometry on \(W^\star\)-algebras ⋮ New computable entanglement monotones from formal group theory ⋮ Geometry from divergence functions and complex structures ⋮ Observables, interference phenomenon and Born’s rule in the probability representation of quantum mechanics ⋮ Tomographic reconstruction of quantum metrics ⋮ Nonlinear dynamics from linear quantum evolutions ⋮ Generalized potential functions in differential geometry and information geometry ⋮ Unitary and nonunitary evolution of qubit states in probability representation of quantum mechanics ⋮ SU(2) and SU(1,1) group parametrizations via qubit induced correlated probabilities ⋮ Lie groupoids in information geometry
Cites Work
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- Classical and quantum Fisher information in the geometrical formulation of quantum mechanics
- Symmetric logarithmic derivative for general \(n\)-level systems and the quantum Fisher information tensor for three-level systems
- Information geometry and its applications
- Star products, duality and double Lie algebras
- Defining the curvature of a statistical problem (with applications to second order efficiency)
- The scalar curvature of the Bures metric on the space of density matrices
- On the Riemannian metric on the space of density matrices
- On the curvature of monotone metrics and a conjecture concerning the Kubo-Mori metric
- On the characterisation of paired monotone metrics
- Monotone metrics on matrix spaces
- Symplectic tomography as classical approach to quantum systems.
- Positive distribution description for spin states.
- Differential-geometrical methods in statistics
- Phase space distributions and a duality symmetry for star products
- GEOMETRY OF MIXED STATES AND DEGENERACY STRUCTURE OF GEOMETRIC PHASES FOR MULTI-LEVEL QUANTUM SYSTEMS: A UNITARY GROUP APPROACH
- Uniqueness of the Fisher–Rao metric on the space of smooth densities
- The volume of Gaussian states by information geometry
- Upper bounds on the relative energy difference of pure and mixed Gaussian states with a fixed fidelity
- On the geometry of mixed states and the Fisher information tensor
- An introduction to the tomographic picture of quantum mechanics
- Symmetries, Group Actions, and Entanglement
- Reconstructing a pure state of a spinsthrough three Stern-Gerlach measurements
- Connections and metrics respecting purification of quantum states
- A CHARACTERISATION OF WIGNER–YANASE SKEW INFORMATION AMONG STATISTICALLY MONOTONE METRICS
- Orbits of quantum states and geometry of Bloch vectors forN-level systems
- Quantum Time Evolution in Terms of Nonredundant Probabilities
- Covariance and Fisher information in quantum mechanics
- Monotone Riemannian metrics on density matrices with non-monotone scalar curvature
- Wigner–Yanase information on quantum state space: The geometric approach
- ON THE ⋆-PRODUCT QUANTIZATION AND THE DUFLO MAP IN THREE DIMENSIONS
- A pedagogical presentation of aC⋆-algebraic approach to quantum tomography
- α-z-Rényi relative entropies
- Information geometry of sandwiched Rényiα-divergence
- Geometries of quantum states
- Nonparametric Information Geometry
- Geometry of quantum systems: density states and entanglement
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