State protection by quantum control before and after noise processes
Hiroaki Wakamura, Ryûitirô Kawakubo, Tatsuhiko Koike · Physical Review A · 2017
We discuss protection of a quantum state that goes through a noise process by measurements and operations before and after the noise process. In our previous work, we showed the nonexistence of ``truly quantum'' protocols that protect an unknown qubit state against depolarizing noise better than ``classical'' ones. Toward identifying the class of noise processes that is optimally suppressed by such a ``classical'' protocol, we extend our previous result in two directions. First, we show that the statement is also true in any finite-dimensional Hilbert spaces, which was previously conjectured; the optimal protocol is either the do nothing protocol or the discriminate and reprepare protocol, depending on the strength of the noise. Second, in the case of a single qubit, we show that essentially the same conclusion holds for any unital noise. Thus, the noise must be nonunital for a control protocol beyond ``classical'' ones to exist.