Classical and Quantum Fisher Information in the Geometrical Formulation of Quantum Mechanics
arXiv:1009.5219 · doi:10.1016/j.physleta.2010.10.005
Abstract
The tomographic picture of quantum mechanics has brought the description of quantum states closer to that of classical probability and statistics. On the other hand, the geometrical formulation of quantum mechanics introduces a metric tensor and a symplectic tensor (Hermitian tensor) on the space of pure states. By putting these two aspects together, we show that the Fisher information metric, both classical and quantum, can be described by means of the Hermitian tensor on the manifold of pure states.
8 pages
References in corpus (11)
- An introduction to the tomographic picture of quantum mechanics
- Fisher information in quantum statistics
- Wigner-Yanase information on quantum state space:the geometric approach
- Geometry of quantum systems: density states and entanglement
- Geometrization of Quantum Mechanics
- On the meaning and interpretation of Tomography in abstract Hilbert spaces
- Geometrical Description of Quantum Mechanics - Transformations and Dynamics
- Maximum Fisher information in mixed state quantum systems
- Differential geometry of density states
- Classical Tensors and Quantum Entanglement I: Pure States
- Geometrisation of Statistical Mechanics
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- Differential Geometry of Quantum States, Observables and Evolution
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