Information between quantum systems via POVMs

Lev B. Levitin, Tommaso Toffoli

Published 2003-06-07, updated 2005-03-12Version 3

The concepts of `conditional entropy' and `information' retain their validity for quantum systems, but their properties differ somewhat from those of their classical counterparts; specifically, some equalities and inequalities of classical information theory are in general violated. In this paper the concepts are generalized to include arbitrary indirect measurements (POVMs). Though the generalization is straightforward, it is important to ascertain that the basic relationships between the generalized quantitites remain the same for the POVMs as for direct measurements.