Abstract
The so-called q-z-Rényi Relative Entropies provide a huge two parameter family of relative entropies which include almost all well-known examples of quantum relative entropies for suitable values of the parameters. In this paper we consider a log-regularized version of this family and use it as a family of potential functions to generate covariant (0,2) symmetric tensors on the space of invertible quantum states in finite dimensions. The geometric formalism developed here allows us to obtain the explicit expressions of such tensor fields in terms of a basis of globally defined differential forms on a suitable unfolding space without the need to introduce a specific set of coordinates. To make the reader acquainted with the intrinsic formalism introduced, we first perform the computation for the qubit case, and then, we extend the computation of the metric-like tensors to a generic n-level system. By suitably varying the parameters q and z, we are able to recover well-known examples of quantum metric tensors that, in our treatment, appear written in terms of globally defined geometrical objects that do not depend on the coordinates system used. In particular, we obtain a coordinate-free expression for the von Neumann–Umegaki metric, for the Bures metric and for the Wigner–Yanase metric in the arbitrary n-level case.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.