Speaker
Lauritz van Luijk, Leibniz University Hanover
Abstract
We generalise the works of Petz and others on sufficiency of *-subalgebras and recovery of quantum channels for quantum statistical experiments from completely positive trace-preserving maps to positive trace-preserving (PTP) maps.
In the PTP setting, the role played by sufficient *-algebras is taken over by sufficient Jordan-*-algebras. For instance, we generalise the interconversion theorem: a quantum statistical experiment is interconvertible via PTP maps with another quantum statistical experiment if and only if their minimal sufficient Jordan-*-algebras are J*-isomorphic. For binary experiments, we show that the minimal sufficient *-algebra and the minimal sufficient Jordan-*-algebra are generated by the Neyman-Pearson tests (the optimal measurements for hypothesis testing). As an application, we obtain that equality in the data-processing inequality of the relative entropy or the alpha-z quantum Rényi divergence implies the existence of a recovery map also in the PTP case.
The talk is based on joint work with Henrik Wilming: arxiv.org/abs/2604.08380 .