Randomization theorems for quantum channels

Understand

The classical randomization criterion is an important result of statistical decision theory.

• Recently, a quantum analogue has been proposed, giving equivalent conditions for two sets of quantum states, ensuring existence of a quantum channel mapping one set close to the other, in $L_1$-distance.
• In the present paper, we extend these concepts in several ways.
• First, sets of states are replaced by channels and randomization is performed by either post- or pre-composition with another channel.