Preservation of a quantum Rényi relative entropy implies existence of a recovery map
Anna Jenčová · Journal of Physics A Mathematical and Theoretical · 2017
Abstract It is known that a necessary and sufficient condition for equality in the data processing inequality (DPI) for the quantum relative entropy is the existence of a recovery map. We show that equality in DPI for a sandwiched Rényi relative α -entropy with α > 1 is also equivalent to this property. For the proof, we use an interpolating family of L p -norms with respect to a state.