The Quantum Blackwell Theorem and Minimum Error State Discrimination

Understand

A quantum analogue of the famous Blackwell Theorem in classical statistics has recently been proposed.

• Given two quantum channels A and B, a set of payoff functions have been proven to have values for B at least as high as they are for A if and only if there exists a quantum garbling channel E such that A=EB.
• When such a channel E exists, we can globally compare A and B in terms of their `noisiness'.
• We show that this method of channel noise comparison is equivalent to one obtained by considering the degradation of the distinguishability of states.