# Tomographic reconstruction of quantum metrics

@article{Laudato2017TomographicRO, title={Tomographic reconstruction of quantum metrics}, author={Marco Laudato and Giuseppe Marmo and Fabio M. Mele and Franco Ventriglia and Patrizia Vitale}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2017}, volume={51} }

In the framework of quantum information geometry we investigate the relationship between monotone metric tensors uniquely defined on the space of quantum tomograms, once the tomographic scheme is chosen, and monotone quantum metrics on the space of quantum states, classified by operator monotone functions, according to the Petz classification theorem. We show that different metrics can be related through a change in the tomographic map and prove that there exists a bijective relation between…

## 9 Citations

### Metric on the space of quantum states from relative entropy. Tomographic reconstruction

- Physics
- 2016

In the framework of quantum information geometry, we derive, from quantum relative Tsallis entropy, a family of quantum metrics on the space of full rank, N level quantum states, by means of a…

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Starting from recent results on the geometric formulation of quantum mechanics, we propose a new information geometric characterization of entanglement for spin network states in the context of…

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- PhysicsJournal of Physics: Conference Series
- 2019

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### Stratified manifold of quantum states, actions of the complex special linear group

- Mathematics, PhysicsAnnals of Physics
- 2019

### Lie groupoids in information geometry

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

We demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one provided by Lie groupoids and Lie algebroids. The contrast…

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- MathematicsOpen Syst. Inf. Dyn.
- 2020

The case when the two-form is degenerate is studied and it is shown how in sufficiently regular cases one reduces it to a pseudometric structures.

### Statistical properties of qutrit in probability representation of quantum mechanics

- PhysicsPhysica A: Statistical Mechanics and its Applications
- 2019

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