The Volume of Two-Qubit States by Information Geometry

Milajiguli Rexiti; Domenico Felice; Stefano Mancini

doi:10.3390/e20020146

The Volume of Two-Qubit States by Information Geometry

Entropy (Basel). 2018 Feb 24;20(2):146. doi: 10.3390/e20020146.

Authors

Milajiguli Rexiti¹, Domenico Felice², Stefano Mancini^{3

4}

Affiliations

¹ School of Advanced Studies, University of Camerino, 62032 Camerino, Italy.
² Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-04103 Leipzig, Germany.
³ School of Science and Technology, University of Camerino, 62032 Camerino, Italy.
⁴ INFN-Sezione di Perugia, I-06123 Perugia, Italy.

Abstract

Using the information geometry approach, we determine the volume of the set of two-qubit states with maximally disordered subsystems. Particular attention is devoted to the behavior of the volume of sub-manifolds of separable and entangled states with fixed purity. We show that the usage of the classical Fisher metric on phase space probability representation of quantum states gives the same qualitative results with respect to different versions of the quantum Fisher metric.

Keywords: Riemannian geometry; entanglement characterization; information theory.