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… 

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

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

Fisher Metric, Geometric Entanglement and Spin Networks

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

Probability representation of quantum mechanics and star product quantization

This paper presents a review of star-product formalism. This formalism provides a description for quantum states and observables by means of the functions called’ symbols of operators’. Those

Geometry from divergence functions and complex structures

Motivated by the geometrical structures of quantum mechanics, we introduce an almost-complex structure $J$ on the product $M\times M$ of any parallelizable statistical manifold $M$. Then, we use $J$

Lie groupoids in information geometry

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

Information geometry on groupoids: the case of singular metrics

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.

References

SHOWING 1-10 OF 34 REFERENCES

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

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

An introduction to the tomographic picture of quantum mechanics

Starting from the famous Pauli problem on the possibility of associating quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair

Geometry of quantum systems: Density states and entanglement

Various problems concerning the geometry of the space of Hermitian operators on a Hilbert space are addressed. In particular, we study the canonical Poisson and Riemann?Jordan tensors and the

A pedagogical presentation of a C⋆-algebraic approach to quantum tomography

It is now well established that quantum tomography provides an alternative picture of quantum mechanics. It is common to introduce tomographic concepts starting with the Schrödinger–Dirac picture of

On the monotonicity of scalar curvature in classical and quantum information geometry

We study the monotonicity under mixing of the scalar curvature for the α-geometries on the simplex of probability vectors. From the results obtained and from numerical data, we are led to some

On the geometry of mixed states and the Fisher information tensor

In this paper, we will review the co-adjoint orbit formulation of finite dimensional quantum mechanics, and in this framework, we will interpret the notion of quantum Fisher information index (and

Monotone metrics on matrix spaces

  • D. Petz
  • Mathematics, Computer Science
  • 1996

Hamilton-Jacobi approach to Potential Functions in Information Geometry

The search for a potential function $S$ allowing to reconstruct a given metric tensor $g$ and a given symmetric covariant tensor $T$ on a manifold $\mathcal{M}$ is formulated as the Hamilton-Jacobi