Metric on the space of quantum states from relative entropy. Tomographic reconstruction
Abstract
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 suitably defined coordinate free differential calculus. The cases N = 2, N = 3 are discussed in detail and notable limits are analyzed. The radial limit procedure has been used to recover quantum metrics for lower rank states, such as pure states. By using the tomographic picture of quantum mechanics we have obtained the Fisher- Rao metric for the space of quantum tomograms and derived a reconstruction formula of the quantum metric of density states out of the tomographic one. A new inequality obtained for probabilities of three spin-1/2 projections in three perpendicular directions is proposed to be checked in experiments with superconducting circuits.
Keywords
Cite
@article{arxiv.1612.07986,
title = {Metric on the space of quantum states from relative entropy. Tomographic reconstruction},
author = {Vladimir I. Man'ko and Giuseppe Marmo and Franco Ventriglia and Patrizia Vitale},
journal= {arXiv preprint arXiv:1612.07986},
year = {2017}
}
Comments
31 pages. No figures. Abstract and Introduction rewritten. Minor corrections. References added