$J$-states and quantum channels between indefinite metric spaces

Raul Felipe-Sosa, Raul Felipe

Published 2020-09-16Version 1

In the present work, we introduce and study states and quantum channels or quantum operators on spaces equipped with an indefinite metric. We will limit the analysis exclusively to the matricial framework. As it will be observed from our considerations, the idea of to build states and quantum channels of indefinite character leads basically to replace, in the customary analysis of these concepts, the usual adjoint of a matrix by its $J$-adjoint which is defined through a $J$-metric where the corresponding matrix $J$ is a fundamental symmetry of $M_{n}(\mathbb{C})$. In particular, for quantum operators, we include in our paper, the general case in the which, they map $J_{1}$-states into $J_{2}$-states where $J_{1}\neq J_{2}$ are two arbitrary fundamental symmetries. In the middle of this program, we carry out a founding study in this context, of the completely positive maps between two different spaces each one provided of an indefinite metric.