Uncertainty principle with quantum Fisher information
arXiv:0707.1147 · doi:10.1063/1.2830429
Abstract
In this paper we prove a nontrivial lower bound for the determinant of the covariance matrix of quantum mechanical observables, which was conjectured by Gibilisco, Isola and Imparato. The lower bound is given in terms of the commutator of the state and the observables and their scalar product, which is generated by an arbitrary symmetric operator monotone function.
8 pages, LaTeX; added references
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Cited by in corpus (10)
- Introduction to quantum Fisher information
- Metric adjusted skew information: Convexity and restricted forms of superadditivity
- From f-divergence to quantum quasi-entropies and their use
- Quantum Fisher Information of an Open and Noisy System in the Steady State
- Inequalities for quantum skew information
- Generalized Wigner-Yanase Skew Information and the Affiliated Inequality
- A Proposal for Quantum Fisher Information Optimization and its Relation with Entanglement Measures
- Quantum covariance, quantum Fisher information and the uncertainty principle
- From quasi-entropy to skew information
- On Negativity and Quantum Fisher Information of an Open and Noisy System in the Steady State