Southwest Quantum Information and Technology

Approximate reversibility in the context of entropy gain, information gain, and complete positivity

Presenting Author: Siddhartha Das, Louisiana State University
Contributing Author(s): Mark M. Wilde

We provide several new limiting entropy bounds in quantum information, by making use of recent advances regarding quantum recoverability and approximate Markovianity. First, we give a lower bound on the entropy gain of a quantum channel in terms of the ``relative entropy distance'' between the channel input and the adjoint of the channel applied to the channel output. This lower bound is non-negative for unital quantum channels and thus significantly strengthens the well known theorem that the entropy gain is non-negative for unital channels. Next, we establish a one-sided information-disturbance inequality that quantitatively demonstrates that there is little disturbance to a quantum state whenever there is little information gained by a quantum measurement. This inequality takes on an operational use in a protocol known as measurement compression with quantum side information. Finally, we show how satisfying the quantum data processing inequality approximately is equivalent to an evolution being approximately completely positive.

(Session 5 : Thursday from 5:00 - 7:00 pm)