Let's say I have a theoretical/ computational process that inverts the outputs of a quantum channel and returns noise-free input density matrices. I perform quantum process tomography on my process and obtain a $\chi$ matrix that has negative eigenvalues (meaning that the process is not CPTP) but $\chi$ is Hermitian and has trace 1.
How do I interpret this $\chi$ matrix then? I think that maybe it means that the inverse map is an HPTP map, but I am not sure because I don't know much about HPTP maps. Any help will be appreciated. Thanks
